The numerical solution of parabolic partial differential equations by the method of integral operators†

Abstract

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 integraloperator solutions of parabolic differential equations are evaluated numerically with ease. The solutions of example problems are given.