Explicit formulae for integro-differential operational matrices. (English) Zbl 1506.42034
Summary: In this work we deduce explicit formulae for the elements of the matrices representing the action of integro-differential operators over the coefficients of generalized Fourier series. Our formulae are obtained by performing operations on the bases of orthogonal polynomials and result directly from the three-term recurrence relation satisfied by the polynomials. Moreover we give exact formulae for the coefficients for some families of orthogonal polynomials. Some tests are given to demonstrate the robustness of the formulas presented.
MSC:
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
| 42A16 | Fourier coefficients, Fourier series of functions with special properties, special Fourier series |
| 47G20 | Integro-differential operators |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
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