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Abstract
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This paper is concerned with a new implementation ofavariant of the finite collocation(FC)method for
solving the 2D time dependent partial differential equations(PDEs)of parabolic type. The time variable is
eliminated by using an appropriate finite difference(FD)scheme.Then,in the resultant elliptic type
PDEs, a combination of the FC and local RBF method is used for spatial discretization of the field variables. Unlike the traditional global RBF collocation method, dividing the collocation of the problem in the
global domain in to many local regions,the method becomes highly stable.Furthermore,the computational cost of the method is modest due to using strong form equation,collocation approach and that the
matrix operations require only inversion of matrices of smallsize.Different approaches are investigated
to impose Neumann's boundary conditions. The test problems consist of three linear convection–diffusion–
reaction equations and a 2D nonlinear Burger'sequation. An iterative approach is proposed to deal
with the nonlinear term of Burger'sequation
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