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Abstract
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This paper is concerned with the development of a new approach for the numerical solution of linear and
nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal
boundary conditions. Proper finite-difference approximations are utilized to discretize the time variable.
Then, the weak equations of resultant elliptic type PDEs are constructed on local subdomains. These local
weak equations are discretized by using the multiquadric (MQ) radial basis function (RBF) approximation
where an iterative procedure is proposed to treat the nonlinear terms in each time step. Numerical test
problems are given to verify the accuracy of the obtained numerical approximations and stability of the
proposed method versus the parameters of the nonlocal boundary conditions.
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