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Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws. (English) Zbl 0991.65072
This paper is concerned with the formulation of conservative finite difference schemes with the total variation diminishing (TVD) property to solve systems of nonlinear hyperbolic conservation laws with source terms.
A technique based on the transformation of the nonhomogeneous problem into a homogeneous form through the definition of a new flux formed by the physical flux and the primitive of the source term is proposed.
The application of the numerical methods described for homogeneous conservation laws needs a new formalization of the classical schemes.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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