Solving Linear And Weakly Nonlinear Parabolic Differential Equations By Krylov Approximation Method

Mathematics Research Report MRR95-067

Solving Linear And Weakly Nonlinear Parabolic Differential Equations By Krylov Approximation Method

Teresa Leyk and David Stewart

Abstract: We present the method for solving linear and weakly nonlinear parabolic PDEs. Space variables are discretized using the finite difference method. The resulting large and sparse system of ODEs is solved by approximating the evolution operator exp(At) on a given state vector. The evolution operator is approximated by a smaller exponential matrix, which is computed using high-order Padé approximations. It will also be shown how the method can be extended to an inhomogenous problem by applying some quadratures. The only operations involving the original large matrix are matrix-by-vector multiplications and as a result, the algorithm can easily be parallelized and vectorized.

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