A matrix formulation of the Tau method for the numerical solution of non-linear problems
Provides a new numerical approach for solving higher-order ODEs, but the improvement over existing methods appears incremental.
The paper introduces the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations, achieving high accuracy and computational simplicity compared to existing methods.
The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted Bessel polynomials on the interval [a, b] are calculated. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ODE to the solution of a system of algebraic equations with unknown Bessel coefficients. The comparisons between the results of the present work and other the numerical method are shown that the present work is computationally simple and highly accurate.