Efficient Computational Methods for Solving the One-Dimensional Parabolic Equation with Nonlocal Initial and Boundary Conditions

Abstract

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica^®12. The techniques of effective computational methods (DECMs) have been applied to solve some specific cases of time-dependent diffusion equations. Moreover, the maximum absolute error () is determined to demonstrate the accuracy of the proposed techniques.