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Science Press, 2004. N. Atluri, S. Shen, The Meshless Local Petrov–Galerkin (MLPG) Method, Tech. Science Press, 2002. N. Atluri, S. Shen, The meshless local Petrov–Galerkin (MLPG) method: a simple and less costly alternative to the finite element and boundary element methods, Comput. Modeling Engrg. Sci. 3 (2002) 11–51. N. L. Zhu, A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics, Comput. Mech. 22 (1998) 117–127. N. L. Zhu, A new meshless local Petrov–Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation, Comput.

Fig. 4. 5 for Example 2. for which the exact solution is u (x, y , t ) = (1 + y ) exp(x + t ), μ(t ) = exp(t ). 025, where r0 is the radius of the local subdomain. 1 and N = 1089 nodes are shown in Table 2. Also Figs. 4 and 5 show the exact and approximate solutions in both algorithms. 6. Conclusions In this paper an MLPG method was proposed for the study of parabolic partial differential equations with Neumann’s and non-classical boundary conditions. Two new techniques, namely Algorithms A and B, were proposed to impose the Neumann’s boundary conditions on square domains.

Cannon, Y. Lin, An inverse problem of finding a parameter in a semi-linear heat equation, J. Math. Anal. Appl. 145 (2) (1990) 470–484. R. Cannon, Y. L. Matheson, The solution of the diffusion equation in two-space variables subject to the specification of mass, Appl. Anal. 50 (1993) 1–19. R. Cannon, J. van der Hoek, Diffusion subject to specification of mass, J. Math. Anal. Appl. 115 (1986) 517–529. [11] V. Capsso, K. Kunisch, A reaction–diffusion system arising in modeling man-environment diseases, Quart.

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Applied Numerical Mathematics 61 (February 2011) by Robert Beauwens, Martin Berzins

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