Block monotone iterations for solving coupled systems of nonlinear parabolic equations
Keywords:Systems of nonlinear parabolic equations, quasi-monotone functions, method of upper and lower solutions, block monotone iterative methods.
The article deals with numerical methods for solving a coupled system of nonlinear parabolic problems, where reaction functions are quasi-monotone nondecreasing. We employ block monotone iterative methods based on the Jacobi and Gauss–Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of a solution are discussed. Numerical experiments are presented.
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