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A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension. (English) Zbl 0779.65058
The numerical method of lines is used to approximate the solution of a system of parabolic partial differential equations (PDEs) in one space dimension. By approximating the spatial derivatives by finite differences on a fixed uniform or nonuniform mesh, the system of PDEs is reduced to a semidiscrete system of ordinary differential equations in the time direction. The resulting system of ordinary differential equations is integrated numerically by a second-order \(L\)-stable composite integration scheme using variable stepsize sequences [cf. the author, ibid. 25, No. 1, 1-13 (1989; Zbl 0664.65072)].
The nonlinear system of algebraic equations resulting from the application of the composite integration scheme is solved using a modified Newton algorithm for a limited number of iterations. A number of numerical experiments is presented.
Reviewer: S.Jiang (Bonn)

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L05 Numerical methods for initial value problems
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
EPDCOL; PDECOL; SPRINT2D
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References:
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