Solving the nonlinear heat equilibrium problems using the local multiquadric radial basis function collocation method

Abstract

In this article, the nonlinear heat equilibrium problems are solved by the local multiquadric (MQ) radial basis function (RBF) collocation method. The system of nonlinear algebraic equations is solved by iteration based on the residual norm-based algorithm, in which the direction of evolution is determined by a linear equation. In addition, the role of the collocation point and source point is clearly defined such that in our proposed method the field value of any interested point can be expressed. Six numerical examples are shown to check the performance of the proposed method. As the number of supporting points (mp) increases, the accuracy of numerical solution increases. Among all examples, mp = 50 can perform well. In addition, the selection of shape parameter, c, affects the accuracy. However, as c < 2 the maximum relative absolute error percentage is less than 1%.