Lax–Wendroff method
E890451
The Lax–Wendroff method is a numerical scheme for solving hyperbolic partial differential equations that achieves second-order accuracy in both space and time by using a Taylor series expansion and flux approximations.
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
finite difference scheme
ⓘ
hyperbolic PDE solver ⓘ numerical method ⓘ |
| accuracyProperty | second-order accurate for smooth solutions ⓘ |
| belongsToField |
computational fluid dynamics
NERFINISHED
ⓘ
computational physics ⓘ numerical analysis ⓘ |
| canBeExtendedTo |
multi-dimensional problems
ⓘ
systems of conservation laws ⓘ |
| discretizationType |
explicit scheme
ⓘ
two-step method ⓘ |
| hasOrderOfAccuracy |
second order in space
ⓘ
second order in time ⓘ |
| introducedInField | numerical solution of hyperbolic conservation laws ⓘ |
| isPrototypeFor | high-resolution shock-capturing schemes ⓘ |
| limitation |
non-monotone near sharp gradients
ⓘ
not TVD without modification ⓘ |
| namedAfter |
Benjamin Wendroff
NERFINISHED
ⓘ
Peter Lax NERFINISHED ⓘ |
| numericalProperty |
can produce spurious oscillations near discontinuities
ⓘ
dispersive ⓘ |
| relatedTo |
Godunov method
NERFINISHED
ⓘ
Lax–Friedrichs method NERFINISHED ⓘ MacCormack method NERFINISHED ⓘ finite volume methods ⓘ |
| solves | hyperbolic partial differential equations ⓘ |
| spaceDiscretization | finite difference in space ⓘ |
| stabilityCondition | CFL condition ⓘ |
| timeDiscretization | finite difference in time ⓘ |
| timeIntegration | single-step second-order method ⓘ |
| typicalApplication |
linear advection equation
ⓘ
shallow water equations ⓘ wave propagation problems ⓘ |
| typicalGrid | uniform spatial grid ⓘ |
| typicalUseCase |
benchmarking numerical schemes for hyperbolic PDEs
ⓘ
modeling linear wave propagation ⓘ |
| usesConcept | flux approximation ⓘ |
| usesIdea |
Taylor expansion in time with spatial derivatives
ⓘ
replacement of time derivatives by spatial derivatives via PDE ⓘ |
| usesMathematicalTool | Taylor series expansion NERFINISHED ⓘ |
Referenced by (1)
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