The method of lines for parabolic partial integro-differential equations. (English) Zbl 0763.65101

The author discusses a method of lines for nonlinear Volterra partial integro-differential equations of parabolic type. In the first step of discretization, a finite difference method is used in the spatial direction to obtain a system of nonlinear stiff Volterra integro- differential equations in time. Then in the second step, this system is numerically integrated in the temporal variable by the implicit Euler method. The concept of logarithmic matrix norm, earlier introduced in the study of numerical methods for nonlinear stiff ordinary differential equations, plays a key role in deriving realistic error bounds in the convergence analysis of this paper. Finally, some numerical results are cited to illustrate the error bounds and the rate of convergence.
Reviewer: A.K.Pani (Bombay)


65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
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