Method of lines for initial value and initial-boundary value problems involving PDEs, Numerical solution of boundary value problems involving ordinary differential equations, waveform relaxation, convergence, algorithm, matrix splitting, method of lines, Parallel numerical computation, 510, domain decomposition, Reaction-diffusion equations, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, reaction diffusion equations, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, mesh refinement, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parallel computation, Stability and convergence of numerical methods for ordinary differential equations, ddc: ddc:510