Two new finite difference schemes for parabolic equations. (English) Zbl 0553.65084
The author takes two extrapolation methods for the numerical solution of partial differential equations and shows that they can be expressed as semi-implicit Runge-Kutta methods. He points out that they are of lower order for nonlinear equations. He finds other semi-implicit methods including a second order three stage diagonally-implicit Runge-Kutta (DIRK) formula given also by R. Alexander [ibid. 14, 1006-1021 (1977; Zbl 0374.65038)] which is not among his references. (This paper does not distinguish between the terms semi-implicit and diagonally implicit.) His numerical results compare various methods for parabolic problems which are stiff or have rapid decay.
Reviewer: J.D.P.Donnelly
MSC:
65N40 | Method of lines for boundary value problems involving PDEs |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
35K20 | Initial-boundary value problems for second-order parabolic equations |
65L05 | Numerical methods for initial value problems involving ordinary differential equations |