The Correct Formulation of Intermediate Boundary Conditions for Runge--Kutta Time Integration of Initial Boundary Value Problems

Authors:
D. Pathria
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

Citing 0
Cited 12

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Abstract

A disturbing feature of applying explicit high-order Runge--Kutta (RK) time integrators to initial boundary value problems solved by the method of lines is the loss of accuracy that results from wrong specifications of intermediate-stage boundary conditions. The solution proposed here is to prescribe analytically those values that would result from applying the RK solver at the boundaries, and hence maintain the order of the RK method without a reduction in the step size limit. The procedure is described in detail for nonlinear hyperbolic equations, and both scalar and vector examples are presented.