Solving differential and integral equations with Tau method
For researchers in numerical analysis, this is an incremental improvement to the operational Tau method by simplifying matrix computation.
This work presents a new approach for implementing the operational Tau method to solve linear differential and integral equations, using three-term recurrence relations of orthogonal polynomials to compute operational matrices. Numerical applications demonstrate the method's effectiveness.
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to compute the operational matrices. We also give numerical applications of operational matrices to solve differential and integral problems using the operational Tau method.