The Numerical Solution of Parabolic Partial Differential Equations by the Method of Integral Operators.

摘要

The numerical solution of parabolic partial differential equations is accomplished by the use of integral operators and a complete family of solutions. This method is one where the kernel of the integral operator and the special solutions of the differential equation are expanded in long (20-term) Taylor series. Once the series for the functions have been obtained, numerical integration can be performed by a term-by-term integration (a simple shifting of terms). Thus, the integral-operator solutions of parabolic differential equations are evaluated numerically with ease. The solutions of example problems are given. (Author)