An Effective Numerical Approach Based on Cubic Hermite B-spline Collocation Method for Solving the 1D Heat Conduction Equation
S. Kutluay, Nuri Murat Yağmurlu, Ali Sercan Karakaş
Abstract
This article is going to deal with the numerical solutions about the most vital problem arising in nature; namely the heat conduction equation given in one-dimension. For this aim, we are going to use cubic Hermite B-spline finite elements based on collocation method. Then, the algorithm of the method has been produced and the stability analysis has also been examined via Fourier stability method. Furthermore, a comparative study between the approximate and exact solutions has been used to demonstrate the accuracy and efficiency of the proposed scheme. The newly obtained results clearly show that the present scheme is a reliable and accurate one and may even be used successfully to find approximate solutions of numerous nonlinear problems encountering widely in many applied sciences.