Improved Second Order Methods for Parabolic Partial Differential Equations

摘要

Two new finite difference for the calculation of parabolic partial differential equations. The leading truncation error terms are derived and detailed comparisons are made with the errors associated with existing methods, namely the Crank-Nicolson method and Keller Box scheme. A number of examples of both linear and non-linear parabolic problems are computed with both the new and also the existing methods. The accuracy of all four methods are compared; based on the computational experiments and a comparison of the magnitudes of the leading truncation errors, it is concluded that the improved methods are to be preferred over the existing methods.