An Advanced Exponential Method for the Solution of Parabolic Differential Equations 2000-01-2486
Many methods have been suggested for the solution of parabolic partial differential equations. Prior efforts have heavily focused on explicit difference equations, implicit difference equations, and a combination of these two methods. Some work has been done in exponential methods and other obscure methods. This paper introduces an advanced exponential method for obtaining solutions of parabolic partial differential equations.
The explicit, implicit, Crank-Nicolson, DuFort-Frankel, modified DuFort-Frankel, original exponential method, and the advanced exponential method are briefly described and compared. The advanced exponential method is unconditionally stable with whatever time step is taken. Accuracy and speed of solution for this method is compared to other solution methods for various example test cases. For the example test cases, the method gave excellent results when compared to the analytical solution and to other methods. The method has been introduced into the Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code as a solver. The advanced exponential method gives excellent speed, accuracy, and stability for solving parabolic partial differential equations.