Novel numerical solutions of nonlinear heat transfer problems using the linear barycentric rational interpolation

What is it about?

In this investigation, a numerical technique to obtain the approximate solutions of four well‐known nonlinear differential equations in the area of heat transfer is presented. This method is based on the operational matrix of derivative of linear barycentric rational interpolation. The main advantages of this approach are that it uses the Floater‐Hormann weights, which are very efficient in practice, and reduces the governing differential equation to a system of algebraic equations. The results are compared with the obtained numerical results of the fourth‐order Runge‐Kutta method along with the shooting method and some of the previously existing methods. The acquired results reveal that the derivative operational matrix method with barycentric rational basis functions is very efficient and can be implemented easily and fast.

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