Numerical solution of the Goursat problem on a triangular domain with mixed boundary conditions |
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| Authors: | Kun Gou Bo Sun |
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| Institution: | a Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
b College of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha, Hunan 410076, PR China |
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| Abstract: | For the Goursat problem, we consider a triangular domain with mixed Dirichlet and impedance boundary conditions imposed on it. We develop an algorithm for its numerical solution mainly based on Runge-Kutta method and trapezoidal formula. Iterative techniques are constructed to compute some data for the nonlinear part of the differential equation and the impedance boundary condition. Error estimates are derived. Examples are presented to illustrate the effectiveness of the method. |
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| Keywords: | Goursat problem Impedance boundary condition Triangular domain |
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