Discretized Picard’s Method
نویسندگان
چکیده
Using the Modified Picard Method of Parker and Sochacki [1, 2], we derive a hybrid scheme using the analytical Picard method with approximations to the differential operators. This new method, called Discretized Picard’s Method, uses approximations in the space dimensions to compute derivatives but utilizes a continuous approximation in the time dimension. We illustrate the method using finite difference schemes on linear and nonlinear PDEs. We derive the stability condition for several examples and show the stability region is increasing up to the CFL condition. Finally, we demonstrate results in one and two dimensions for this method.
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