Numerical Solution of the Burgers’ Equation Using Chelyshkov Polynomials

Abstract The paper proposes a numerical method to approximate the solution of the nonlinear Burgers’ equation. The approach utilizes the Crank-Nicolson scheme for temporal discretization, leading to a discrete formulation and approximations of the solution at each time step. These approximations are then expressed using the Chelyshkov polynomial basis. The system of nonlinear equations resulting from this transformation is solved using Newton’s method to determine the unknowns. To evaluate the effectiveness and accuracy of the proposed method, three numerical examples are presented. A comparison with existing literature demonstrates that the method is more accurate and efficient in producing calculations. AMS 33C45, 65N06, 65M70.