| [1] |
Kupradze, V. D.; Aleksidze, M. A., The method of functional equations for the approximate solution of certain boundary value problems, USSR Comput Math Math Phys, 4, 82-126 (1964) · Zbl 0154.17604 |
| [2] |
Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv Comput Math, 9, 69-95 (1998) · Zbl 0922.65074 |
| [3] |
Golberg, M. A.; Chen, C. S., The method of fundamental solutions for potential, helmholtz and diffusion problems, (Golberg, M. A., Boundary integral methods: numerical and mathematical aspects (1998), WIT Press), 103-176 · Zbl 0945.65130 |
| [4] |
Chen, C. S.; Fan, C. M.; Wen, P. H., The method of particular solutions for solving certain partial differential equations, Numer Methods Partial Differential Equations, 28, 506-522 (2010) · Zbl 1242.65267 |
| [5] |
Chen, C. S.; Fan, C. M.; Wen, P. H., The method of approximate particular solutions for solving elliptic problems with variable coefficients, Int J Comput Methods, 8, 3, 545-559 (2011) · Zbl 1245.65172 |
| [6] |
Chen, C. S.; Fan, C. M.; Wen, P., The method of fundamental solutions for solving elliptic PDEs with variable coefficients, (Chen, C. S.; Karageorghis, A.; Smyrlis, Y., The method of fundamental solutions- a meshless method (2008), Dynamic System Inc.: Dynamic System Inc. Atlanta), 75-105 |
| [7] |
Morton, K. W.; Mayers, D. F., Numerical solution of PDEs, an introduction (2005), Cambridge University Press · Zbl 1126.65077 |
| [8] |
Reddy, J. N., An introduction to the finite element method (2006), McGraw Hill |
| [9] |
LeVeque, R., Finite volume methods for hyperbolic problems (2002), Cambridge University Press · Zbl 1010.65040 |
| [10] |
Yao, G.; Kolibal, J.; Chen, C. S., A localized approach for the method of approximate particular solutions, Comput Math Appl, 61, 2376-2387 (2011) · Zbl 1221.65316 |
| [11] |
Sarler, B.; Vertnik, R., Meshfree explicit local radial basis function collocation method for diffusion problems, Comput Math Appl, 51, 1269-1282 (2006) · Zbl 1168.41003 |
| [12] |
Yao, G.; Chen, C. S.; Zheng, H., A modified method of approximate particular solutions for solving linear and nonlinear PDEs, Numer Methods Partial Differential Equations, 33, 1839-1858 (2017) · Zbl 1383.65147 |
| [13] |
Khatri Ghimire, B.; Lamichhane, A. R.; Watson, D.; Zhou, Z., Solving fourth-order partial differential equations using radial basis function collocation methods, Neural, Parallel, Sci Comput, 25, 91-106 (2017) |
| [14] |
Zhang, L. P.; Li, Z. C.; Chen, Z.; Huang, H. T., The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions, Appl Numer Math, 154, 47-69 (2020) · Zbl 1437.35184 |
| [15] |
Fornberg, B.; Larson, E.; Wright, G., A new class of oscillatory radial basis functions, Comput Math Appl, 51, 1209-1222 (2006) · Zbl 1161.41304 |
| [16] |
Lamichhane, A. R.; Khatri Ghimire, B.; Wakayama, Y.; Sube, A., The closed-form particular solutions for the Laplace operator using oscillatory radial basis functions in 2D, Eng Anal Bound Elem, 96, 187-193 (2018) · Zbl 1403.65166 |
| [17] |
Abramowitz, M.; Stegun, I., Handbook of mathematical functions with formulas, graphs, and mathematical tables (1964), Dover · Zbl 0171.38503 |
| [18] |
Fasshauer, G.; Zhang, J., On choosing optimal shape parameters for RBF approximation, Numer Algorithms, 45, 345-368 (2007) · Zbl 1127.65009 |
| [19] |
Sarra, S. A.; Sturgill, D., A random variable shape parameter strategy for radial basis function approximation methods, Eng Anal Bound Elem, 33, 1239-1245 (2009) · Zbl 1244.65192 |
