Numerical methods for systems of nonlinear integro-parabolic equations of Volterra type. (English) Zbl 1349.65269

Boglaev, Igor

J. Integral Equations Appl. 28, No. 3, 309-342 (2016).

Summary: This paper deals with the numerical solution of systems of nonlinear integro-parabolic problems of Volterra type. The numerical approach is based on the method of upper and lower solutions. A monotone iterative method is constructed. Existence and uniqueness of a solution to the nonlinear difference scheme are established. An analysis of convergence rates of the monotone iterative method is given. Construction of initial upper and lower solutions is discussed. Numerical experiments are presented.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M22	Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65R20	Numerical methods for integral equations

Keywords:

system of nonlinear integro-parabolic equations of Volterra type; nonlinear difference schemes; monotone iterative method; upper and lower solutions