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MOL solvers for hyperbolic PDEs with source terms. (English) Zbl 0986.65084

The authors consider the applications of the algorithm of the method of lines (MOL) to convection-reaction problems modelled by first order hyperbolic equations with stiff source terms (PDEs). Monotone spatial discretisation schemes with space/time error balancing, in which the advective terms are treated explicitly by applying the second-order limited discretisation, are used to reduce the PDEs to a system of ordinary differential equations (ODEs) in time. The backward Euler method and a Gauss-Seidel iteration for the source terms alone are applied to provide an efficient solver for the system of the ODEs. Numerical experiments are presented to illustrate the performance of the method.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
65Y20 Complexity and performance of numerical algorithms

Software:

nag
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Full Text: DOI

References:

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