Radial basis function generated finite difference method for the solution of sinh-Gordon equation
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KünyeRashidinia, J. & Rasoulizadeh, M. N. (2021). Radial basis function generated finite difference method for the solution of sinh-Gordon equation. TWMS Journal of Applied and Engineering Mathematics, 11(3), 893-905.
Accuracy of radial basis functions (RBFs) is increased as the shape parameter decreases and produces an ill-conditioned system. To overcome such difficulty, the global stable computation with Gaussian radial basis function-QR (RBF-QR) method was introduced for a limited number of nodes. The main aim of this work is to develop the stable RBF-QR-FD method in order to obtain numerical solutions for the (1 + 2)-dimensional nonlinear sinh-Gordon (ShG) equation. The efficiency and accuracy of the presented approach are tested by three examples. A comparison between our results and the three methods such as, RBFs collocation based on Kansa’s (RBFK) approach, RBF-Pseudo spectral (RBFPS) and moving least squares (MLS) methods are shown. Furthermore, the stability analysis is proven.
KaynakTWMS Journal of Applied and Engineering Mathematics
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