A CLOSE APPROXIMATION OF THE SOLUTION TO THE HEAT EQUATION CONTAINING A DEPENDENT LINEAR CONVECTION FACTOR USING THE DOUBLE INTERPOLATION METHOD    

Authors : 1DIWARI LAL; 2KRISHAN KANT SINGH

Publishing Date : 2023

DOI : https://doi.org/10.52458/9789388996570.2023.eb.ch045

ISBN : 978-93-88996-58-7

Pages : 241

Chapter id : NSP/ICAAR-2023/A-45

Abstract : The heat equation is an example of a partial differential equation that can be used to describe the time-dependent concentration gradient across a domain of some quantity (like heat, for example). In this study, the dependent source term in the heat equation and its solution are the primary focuses of our attention. In the interest of transparency, we will assume that the source term is linear. Let's have a look at an example to better understand this topic. Due to the complexity of the underlying source terms, the answer cannot be reached by the process of variable separation. The double interpolation method is one of the novel approaches that we have investigated in order to solve the heat equation which has a dependent source term. By applying the formula for the recurrence relation in finite differences, we were able to determine the values of u(x,t) at each point on the lattice. Both the twofold interpolation method and the numerical answer have been examined side by side in this graphic comparison that we have created.

Keywords : heat equation, convection term, double interpolation method

Cite : Lal, D., & Singh, K. K. (2023). A Close Approximation Of The Solution To The Heat Equation Containing A Dependent Linear Convection Factor Using The Double Interpolation Method (1st ed., p. 241). Noble Science Press. https://doi.org/10.52458/9789388996570.2023.eb.ch045

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