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Numerical method for ordinary differential equations
and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary
Backward_Euler_method
Approach to finding numerical solutions of ordinary differential equations
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary
Euler_method
Methods used to find numerical solutions of ordinary differential equations
Euler method (or forward Euler method, in contrast with the backward Euler method, to be described below). The method is named after Leonhard Euler who
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Approaches for approximating solutions to differential equations
explicit formula for y k + 1 {\displaystyle y_{k+1}} . Backward Euler method With the backward Euler method y k + 1 − y k Δ t = − y k + 1 2 {\displaystyle {\frac
Explicit_and_implicit_methods
Finite difference method for numerically solving parabolic differential equations
less accurate backward Euler method is often used, which is both stable and immune to oscillations.[citation needed] The Crank–Nicolson method is based on
Crank–Nicolson_method
Modification of the Euler method for solving Hamilton's equations
Euler method, also called symplectic Euler, semi-explicit Euler, Euler–Cromer, and Newton–Størmer–Verlet (NSV), is a modification of the Euler method
Semi-implicit_Euler_method
Numerical method for solving ordinary differential equations
{\displaystyle y_{n+1}-y_{n}=hf(t_{n+1},y_{n+1})} (this is the backward Euler method) BDF2: y n + 2 − 4 3 y n + 1 + 1 3 y n = 2 3 h f ( t n + 2 , y n
Backward differentiation formula
Backward_differentiation_formula
Class of iterative numerical methods for solving differential equations
listed, where the first two methods are the backward Euler method and the trapezoidal rule (also known as the Crank-Nicolson method) respectively: y n = y
Linear_multistep_method
Euler method, a method for finding numerical solutions of differential equations Semi-implicit Euler method Euler–Maruyama method Backward Euler method Euler's
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Family of implicit and explicit iterative methods
Runge–Kutta methods (English: /ˈrʊŋəˈkʊtɑː/ RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used
Runge–Kutta_methods
they can suffer from order reduction. The first order method is similar to the backward Euler method and given by 0 1 1 {\displaystyle {\begin{array}{c|cc}0&1\\\hline
List_of_Runge–Kutta_methods
Interplay between observation, experiment, and theory in science
The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental
Scientific_method
Determining all voltages and currents within an electrical network
{\displaystyle x'(t_{n+1})\approx {\frac {x_{n+1}-x_{n}}{h_{n+1}}}} for the backward Euler method, where hn+1 is the time step. If all circuit components were linear
Network analysis (electrical circuits)
Network_analysis_(electrical_circuits)
every step Backward Euler method — implicit variant of the Euler method Trapezoidal rule — second-order implicit method Runge–Kutta methods — one of the
List of numerical analysis topics
List_of_numerical_analysis_topics
Eratosthenes Sieve of Sundaram Backward Euler method Euler method Linear multistep methods Multigrid methods (MG methods), a group of algorithms for solving
List_of_algorithms
Conversion of continuous functions into discrete counterparts
T}\approx (\mathbf {I} -\mathbf {A} T)^{-1}} , otherwise known as the backward Euler method and e A T ≈ ( I + 1 2 A T ) ( I − 1 2 A T ) − 1 {\displaystyle e^{\mathbf
Discretization
Algorithms in numerical analysis
(known as Heun's method) can be constructed from the Euler method (an explicit method) and the trapezoidal rule (an implicit method). Consider the differential
Predictor–corrector_method
Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation
Deep backward stochastic differential equation method
Deep_backward_stochastic_differential_equation_method
Equation in computational fluid dynamics
x}}\left(u_{i}^{p}-u_{i-1}^{p}\right)} The MacCormack method is well suited for nonlinear equations (Inviscid Burgers' equation, Euler equations, etc.) The order of differencing
MacCormack_method
from method to method. Finite differences are usually the cheapest on a per grid point basis followed by the finite element method and spectral method. However
Numerical methods in fluid mechanics
Numerical_methods_in_fluid_mechanics
Class of numerical techniques
equation u ′ ( x ) = 3 u ( x ) + 2. {\displaystyle u'(x)=3u(x)+2.} The Euler method for solving this equation uses the finite difference quotient u ( x +
Finite_difference_method
Inverse of a finite difference
{\displaystyle B_{1}=-{\tfrac {1}{2}}} . The Euler–Maclaurin formula provides an asymptotic expansion for the inverse backward difference ∇ − 1 f ( x ) = ∑ k = 1
Indefinite_sum
Software able to infer logical consequences
API (JSR 94). EYE, a reasoning engine performing forward- and backward-chaining along Euler paths, supporting the Semantic Web Stack and implementing Notation3
Semantic_reasoner
Differential equation exhibiting high rate of dissipation
Among multistep methods the best choice for stiff equations are the backward differentiation (BDF) methods, to which the implicit Euler method belongs. There
Stiff_equation
Optimization algorithm
exploration of a solution space. Gradient descent can be viewed as applying Euler's method for solving ordinary differential equations x ′ ( t ) = − ∇ f ( x (
Gradient_descent
Formula relating stochastic processes to partial differential equations
and W t {\displaystyle W_{t}} is a Wiener process. Then using the Euler-Maruyama method, the SDE can be numerically integrated forwards in time from the
Feynman–Kac_formula
Study of the rates of chemical reactions
solve the differential equations with Euler and Runge-Kutta methods we need to have the initial values. Euler method → simple but inaccurate. At any point
Chemical_kinetics
Technique for the generative modeling of a continuous probability distribution
use any of the numerical integration methods, such as Euler–Maruyama method, Heun's method, linear multistep methods, etc. Just as in the discrete case
Diffusion_model
Mumerical method for solving differential equations
scheme, which is derived by applying the symplectic Euler method to each independent variable. The Euler box scheme uses a splitting of the skew-symmetric
Multisymplectic_integrator
Method in the dynamics of blood flow
H.; Jones, C. J. H. (1990). "Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics". Journal of Biomechanical
Wave_intensity_analysis
Numerical integration method
by the Euler–Maclaurin summation formula. Several techniques can be used to analyze the error, including: Fourier series Residue calculus Euler–Maclaurin
Trapezoidal_rule
Movement of an object which leaves at least one point unchanged
as the movement obtained by changing one of the Euler angles while leaving the other two constant. Euler rotations are never expressed in terms of the external
Rotation
Process of reconstructing the positions of tectonic plates in the geological past
At earlier stages of Earth's history, new Euler poles need to be defined. In order to move plates backward in time it is necessary to provide information
Plate_reconstruction
Computer graphics technique
Render the shadow volumes (only their back faces are rendered). According to Euler characteristic, all lit surfaces will correspond to a 0 in the stencil buffer
Shadow_volume
Necessary condition for optimality associated with dynamic programming
a system of difference equations or differential equations called the 'Euler equations'. Standard techniques for the solution of difference or differential
Bellman_equation
(1): 109–114. CiteSeerX 10.1.1.422.7691. doi:10.1016/j.jqsrt.2003.10.001. "Euler-Darboux Equation". MathWorld. Retrieved 2009-11-14. Maslov, V. P. (1983)
List of scientific equations named after people
List_of_scientific_equations_named_after_people
Numerical technique
and for other wave-type equations, such as elastodynamics, the linearized Euler equations, Helmholtz equations, and poroelasticity. Berenger's original
Perfectly_matched_layer
Concept in applied mathematics
convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right side of the convection-diffusion
Central_differencing_scheme
∞ {\displaystyle \rho _{\infty }} -Bathe method was developed by replacing the 3-point Euler backward method in the second sub-step with a general formula:
Composite methods for structural dynamics
Composite_methods_for_structural_dynamics
Physics problem related to laws of motion and gravity
reviewing the mathematical history of the problem, mentions that Euler had given a method for integrating a certain differential equation "in 1740 (seven
Three-body_problem
Number of independent parameters needed to define the state of a mechanical system
3T3R consisting of three translations 3T and three rotations 3R. See also Euler angles. For example, the motion of a ship at sea has the six degrees of
Degrees of freedom (mechanics)
Degrees_of_freedom_(mechanics)
Differential equations involving stochastic processes
methods for solving stochastic differential equations include the Euler–Maruyama method, Milstein method, Runge–Kutta method (SDE), Rosenbrock method
Stochastic differential equation
Stochastic_differential_equation
British mathematician (1885–1977)
Cambridge, and widely recognised as on a par with other geniuses such as Euler and Jacobi. In the late 1930s, as the prospect of war loomed, the Department
John_Edensor_Littlewood
Tool to study dynamic behavior of interconnected rigid or flexible bodies
a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of
Multibody_system
Mathematical function
jcp.2006.03.034 Roe, P.L. (1986), "Characteristic-based schemes for the Euler equations", Annu. Rev. Fluid Mech., 18: 337–365, Bibcode:1986AnRFM..18.
Flux_limiter
Early Wright Brothers aircraft
A forward-backward movement controlled the rudder, while a sideways or left-and-right motion controlled wing-warping. In the Orville Method, moving the
Wright_Model_A
cross-stress. Navier–Stokes equations Large eddy simulation Finite element method Backward differentiation formula Computational fluid dynamics Streamline upwind
Variational_multiscale_method
Numerical method for differential equations
solution of the linear ODEs. The recursion (4.3) is also known as Exponential Euler discretization. For a time discretization ( t ) h , {\displaystyle (t)_{h}
Local_linearization_method
Technique for the generative modeling of a discrete probability distribution
backward process requires integration over continuous time. Using the Gillespie algorithm, or other discrete-time algorithms, produces a Euler method
Discrete_diffusion_model
Hungarian philosopher of mathematics and science (1922–1974)
mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties
Imre_Lakatos
His favourite party trick was to read a newspaper column then recite it backward. Winnie Bamara, Australian indigenous woman whose ability to paint scenes
List of people claimed to possess an eidetic memory
List_of_people_claimed_to_possess_an_eidetic_memory
Partial differential equation
Einstein relation. The integration of this equation was done using the Euler–Maruyama method to numerically approximate the path of this Brownian particle. Being
Fokker–Planck_equation
Origin and evolution of the symbols used to write equations and formulas
which means perimeter in Greek. This usage was popularized in 1737 by Euler. In 1734, Pierre Bouguer used double horizontal bar below the inequality
History of mathematical notation
History_of_mathematical_notation
is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed by
List of finite element software packages
List_of_finite_element_software_packages
Product of numbers from 1 to n
count the trailing zeros of the factorials. Daniel Bernoulli and Leonhard Euler interpolated the factorial function to a continuous function of complex
Factorial
Force perpendicular to flow of surrounding fluid
lift. The Euler equations are the NS equations without the viscosity, heat conduction, and turbulence effects. As with a RANS solution, an Euler solution
Lift_(force)
Pictorial representation of the behavior of subatomic particles
lines: this is the Euler algorithm to 2-color a graph, which works whenever each vertex has even degree. The number of steps in the Euler algorithm is only
Feynman_diagram
Property of a mathematical space
basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these
Dimension
Stochastic volatility model used in derivatives markets
simulation schemes are typically considered, like Euler–Maruyama or Milstein. Recently, novel methods have been proposed for the almost exact Monte Carlo
SABR_volatility_model
Theoretical framework in physics
operator, and m is a real parameter (the "mass" of the field). Applying the Euler–Lagrange equation on the Lagrangian: ∂ ∂ t [ ∂ L ∂ ( ∂ ϕ / ∂ t ) ] + ∑ i
Quantum_field_theory
process CIR process / Mar Doléans-Dade exponential Dynkin's formula Euler–Maruyama method Feynman–Kac formula Filtering problem Fokker–Planck equation / Mar
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Fundamental concept of classical mechanics
{\displaystyle \mathbf {F} '_{\mathrm {Euler} }=-m{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '} (Euler force), F C o r i o l i s ′ = − 2 m ω ×
Inertial_frame_of_reference
Polish physicist and mathematician (1931–2022)
(1980). "The Euler-Lagrange resolution". In García, P. L.; Pérez-Rendón, A.; Souriau, J. M. (eds.). Differential Geometrical Methods in Mathematical
Włodzimierz_Marek_Tulczyjew
Programming language
began working on his dissertation with Helmut Weber on the Euler programming language. Euler was based on ALGOL's syntax and many concepts but was not
Pascal_(programming_language)
American annual computer science prize
Niklaus Wirth "for developing a sequence of innovative computer languages, EULER, ALGOL-W, MODULA and PASCAL" University of Zurich 1985 Richard M. Karp "for
Turing_Award
German polymath (1646–1716)
between them and is altered if those distances are altered, his admirer Euler, in the famous 1736 paper solving the Königsberg Bridge Problem and its
Gottfried_Wilhelm_Leibniz
Process of pushing material through a die to create long symmetrical-shaped objects
direction) and backward (ram and billet move in the opposite direction) micro-extrusion was first introduced, with forward rod-backward cup and double
Extrusion
Japanese figure skater (born 1994)
Helsinki 2018. Hanyu is also the first skater to land a quadruple toe loop-Euler-triple flip combination at Skate Canada 2019. At the 2022 Winter Olympics
Yuzuru_Hanyu
Force resisting sliding motion
This view was further elaborated by Bernard Forest de Bélidor and Leonhard Euler (1750), who derived the angle of repose of a weight on an inclined plane
Friction
List of x86 microprocessor instructions
Intel, US Patent 5701442A: Method of modifying an instruction set architecture of a computer processor to maintain backward compatibility, granted in 1997
List_of_x86_instructions
Differential equation for the description of waves or standing wave
integral. One perturbation gives the forward solution, and the other the backward solution. The forward solution gives G ( t , x ) = 1 ( 2 π ) D ∫ sin
Wave_equation
Empress of Russia from 1762 to 1796
54 M. B. W. Trent, "Catherine the Great Invites Euler to Return to St. Petersburg." in Leonhard Euler and the Bernoullis (AK Peters/CRC Press, 2009) pp
Catherine_the_Great
Segment in a figure skating competition
jump or a different double or triple jump in their combination jump. An Euler jump is not allowed in the jump combination in the short program. A skater
Short program (figure skating)
Short_program_(figure_skating)
Mathematical concept
n}}}}{n^{1/4}}}\right).} A Graduate Introduction to Numerical Methods From the Viewpoint of Backward Error Analysis by Corless, Robert, Fillion, Nicolas Alkauskas
Gauss–Kuzmin–Wirsing_operator
superstring 3. World-sheet metric γab(σ,τ) 4. Photon 5. Euler constant .57721... Γ 1. Lattice 2. Euler Gamma function 3. Dirac matrix 4. Width of some scattering
Glossary_of_string_theory
English mathematician (1616–1703)
from the positive side. Wallis was not alone in this thinking: Leonhard Euler came to the same conclusion by considering the geometric series 1 1 − x
John_Wallis
Frame-dependent apparent force in Physics
relative to the rotating frame, such as a wind parcel on Earth; and the Euler force, which arises when a rotating system changes its angular velocity
Fictitious_force
South African cardiac surgeon (1922–2001)
Union, pages 208–09 in which Pravda states, "in spite of South Africa's backward place in the community of nations, positive, creative forces seem to thrive
Christiaan_Barnard
State of matter
suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon
Liquid
Signals broadcast by GPS satellites
where real and imaginary components are both sinusoids as described by Euler's formula. The replica that generates the highest magnitude of dot product
GPS_signals
Continuous progression from past to future
equations, the change in entropy occurs symmetrically whether going forward or backward in time. So entropy tends to increase in either direction, and our current
Time
Russian mathematician (1937–2008)
realize in the p {\displaystyle p} -adic form the «embedding principle» of Euler-Vinogradov and to compute a p {\displaystyle p} -adic analog of Vinogradov
Anatoly_Karatsuba
Computational problem
the configuration requires 6 parameters: (x, y, z) for translation, and Euler angles (α, β, γ). If the robot is a fixed-base manipulator with N revolute
Motion_planning
Mathematical theory about infinitely iterated function composition
contour theory in image processing, and are simple generalizations of the Euler method The series defined recursively by fn(z) = z + gn(z) have the property
Infinite compositions of analytic functions
Infinite_compositions_of_analytic_functions
detection Ethernet Ethical code Euclidean geometry Euler–Lagrange equation Euler's formula Euler's identity Exponential stability Extended Kalman filter
Index of electrical engineering articles
Index_of_electrical_engineering_articles
developed the describing function method as an approximate procedure for analyzing nonlinear control problems. Leonhard Euler Developed the Laplace transform
List of people in systems and control
List_of_people_in_systems_and_control
Traditional board game for two players
to avoid the creation of pawn weaknesses such as isolated, doubled, or backward pawns—and to force such weaknesses in the opponent's position. Most players
Chess
Arithmetic mean is greater than or equal to geometric mean
Nichita, F.F.; Pasarescu, O. Unification Theories: Means and Generalized Euler Formulas. Axioms 2020, 9, 144. Arthur Lohwater (1982). "Introduction to
AM–GM_inequality
Motion of a curve based on its curvature
empirical comparison of the forward Euler, backward Euler, and more accurate Crank–Nicolson finite difference methods, see Balažovjech & Mikula (2009).
Curve-shortening_flow
Interpretation of electrodynamics
in the calculus of variations, and thus it gives no contribution to the Euler–Lagrange equations. Thanks to this result the advanced potentials can be
Wheeler–Feynman absorber theory
Wheeler–Feynman_absorber_theory
Material designed to manipulate sound waves
as the negative or positive state of ρ and β determine the forward or backward wave propagation. In electromagnetic metamaterials negative permittivity
Acoustic_metamaterial
Order of mammals
shifts backward during chewing. The incisors do the gnawing while molars chew; however, due to the cranial anatomy of rodents, these feeding methods cannot
Rodent
Trade bloc of five post-Soviet states
due to Russia's traditional orientation towards Europe and the region's backward infrastructure and underdeveloped economy. In 2012 Russian president Vladimir
Eurasian_Economic_Union
Experiments proving existence of atomic nuclei
¯ n ) 2 {\displaystyle e^{-(90/{\bar {\theta }}_{n})^{2}}} where e is Euler's number (≈2.71828...). A gold foil with a thickness of 1.5 micrometers would
Rutherford scattering experiments
Rutherford_scattering_experiments
French mathematician (born 1956)
improvements of such results. With Bertrand Mercier, Lions proposed a "forward-backward splitting algorithm" for finding a zero of the sum of two maximal monotone
Pierre-Louis_Lions
Mental disorder with psychotic symptoms
perception that is consistently found in schizophrenia is that of visual backward masking. Visual processing impairments include an inability to perceive
Schizophrenia
List of definitions of terms and concepts commonly used in aerospace engineering
Space Agency ET – (Space Shuttle) external tank Euler angles – are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Study of biochemical reaction rates catalysed by an enzyme
achieved, however, if one recognises the problem associated with the use of Euler's number in the description of first order chemical kinetics. i.e. e−k is
Enzyme_kinetics
Adages and sayings named after a person
technology. The name "Eroom" is "Moore" spelled backward, in order to contrast it with Moore's law. Euler's laws of motion: extends Newton's laws of motion
List_of_eponymous_laws
Curved path of an object around a point
progress on the three-body problem, discovering the Lagrangian points with Euler. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier
Orbit
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
Boy/Male
French, German, Irish
Dominant Ruler; Powerful Ruler
Boy/Male
Australian, British, English
One who Packs
Boy/Male
Christian, German, Norse, Polish, Scandinavian, Swedish
Peaceful Ruler; Forever; Alone; Ruler; All-ruler
Boy/Male
Danish, German, Swedish
Island Ruler; Ever Ruler
Boy/Male
German, Swedish
Ever Ruler; Island Ruler
Boy/Male
French, German
Wise Ruler; Old Ruler; Long Term Ruler
Boy/Male
American, Australian, British, English
Strong Guardian
Girl/Female
Scottish
Backward spelling of Agnes: pure; chaste.
Girl/Female
American, Australian, Chinese, Christian, French
Alone Spelled Backwards; Solitary; Magnolia
Boy/Male
Australian, Dutch, French, German, Italian, Latin, Swiss
Powerful Ruler; Dominant Ruler
Boy/Male
German
Powerful Ruler; Army Ruler
Boy/Male
American, British, English
Royal Ruler; King's Ruler
Surname or Lastname
English, Scottish, and northern Irish
English, Scottish, and northern Irish : of uncertain etymology: perhaps a derivative of the nickname black heart, or from blackguard, a Tudor term denoting a group of the lowest-class menials in a household.Perhaps also an altered spelling of German Blackert.
Boy/Male
German, Teutonic
Hardworking Ruler; Home Ruler
Boy/Male
British, English
Wheel Ruler; Circle Ruler
Boy/Male
American, Chinese, Christian, Danish, French, German, Norse, Scandinavian, Swedish
Ruler; Ruler of the People; Peaceful Ruler; All-ruler; Forever; Alone; Ever Ruler
Boy/Male
American, Czech, Danish, French, German, Scandinavian, Swedish
Honourable Ruler; Peaceful Ruler; All Ruler; Ever Ruler
Boy/Male
American, Anglo, British, Christian, English, German
Wealthy Ruler; Rich Ruler
Boy/Male
Christian, German, Teutonic
Hard Working Ruler; Industrious Ruler; Home Ruler
Surname or Lastname
English
English : from Middle English pa(c)k ‘pack’, ‘bundle’ + the Anglo-Norman French pejorative suffix -ard, hence a derogatory occupational name for a peddler.English : pejorative derivative of the Middle English personal name Pack.English : from a Norman personal name, Pachard, Baghard, composed of the Germanic elements pac, bag ‘fight’ + hard ‘hardy’, ‘brave’, ‘strong’.Probably an Americanized spelling of German Packert, Päckert, from Germanic personal names formed with a word meaning ‘battle’ or ‘to fight’; or a variant of Packer 2 (with excrescent -t).
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
Girl/Female
Indian
Exalted, Noble, Highest social standing
Boy/Male
Hindu, Indian, Malayalam, Marathi, Sindhi
Mountain of Gold
Boy/Male
Tamil
Nagarathna | நாகரதநா
Snakes diamond
Girl/Female
Indian, Telugu
River Name
Boy/Male
Hindu, Indian, Sanskrit
Gods Name
Boy/Male
Irish
From the knolls.
Female
French
French form of Roman Latin Lucia, LUCIE means "light."Â
Girl/Female
Hindu, Indian
Nice
Boy/Male
English American
rules by the spear.
Male
English
Middle English form of Low German Lammert, LAMBERT means "land-bright."
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
BACKWARD EULER-METHOD
a. & adv.
Somewhat late; backward.
a.
See Awkward.
a.
Wanting dexterity in the use of the hands, or of instruments; not dexterous; without skill; clumsy; wanting ease, grace, or effectiveness in movement; ungraceful; as, he was awkward at a trick; an awkward boy.
a.
Slow; sluggish; backward.
n.
A turning or bending backward; also, the state of being turned or bent backward; displacement backwards; as, retroversion of the uterus.
adv.
In a contrary or reverse manner, way, or direction; contrarily; as, to read backwards.
superl.
Backward; slow.
a.
Backward.
adv.
With the back in advance or foremost; as, to ride backward.
v. i.
Suffixes denoting course or direction to; motion or tendency toward; as in backward, or backwards; toward, or towards, etc.
a.
Not advanced in civilization; undeveloped; as, the country or region is in a backward state.
adv.
Toward the back; toward the rear; as, to throw the arms backward.
a.
Late or behindhand; as, a backward season.
v. i.
To keep back; to hinder.
a.
Directed to the back or rear; as, backward glances.
n.
A backward stroke.
adv.
Backward.
a.
Not well advanced in learning; not quick of apprehension; dull; inapt; as, a backward child.
adv.
Alt. of Backwards
adv.
Backward; in a backward direction; as, emitted aversely.