Numerical solution of the Goursat problem on a triangular domain with mixed boundary conditions

• Published in: Applied mathematics and computation Vol. 217; no. 21; pp. 8765 - 8777
• Main Authors: Gou, Kun, Sun, Bo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-07-2011; Elsevier
• Subjects: Algorithms; Boundary conditions; Differential equations; Dirichlet problem; Estimates; Exact sciences and technology; Goursat problem; Impedance; Impedance boundary condition; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Runge-Kutta method; Sciences and techniques of general use; Triangular domain; Triangular domain; Impedance boundary condition; Goursat problem; Error estimation; Differential equation; Iterative method; Boundary condition; Runge Kutta method; Algorithm; Non linear equation; Extrapolation; Numerical analysis; Multistep method; Applied mathematics; Numerical solution
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2011.03.129

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.