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How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems
BIT Numerical Mathematics. 2022, V. 62, n. 2, p. 431-463
Fecha de publicación
It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation on the boundary. However, in a previous paper, a modification of Lawson quadrature rules has been suggested so that no order reduction turns up when integrating linear problems subject to time-dependent boundary conditions. In this paper, we describe and thoroughly analyse a technique to avoid also order reduction when integrating nonlinear problems. This is very useful because, given any Runge–Kutta method of any classical order, a Lawson method can be constructed associated to it for which the order is conserved.
Initial boundary value problems
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