Abstract
Operational Jacobi Galerkin method is developed and analyzed to solve multiple delay pantograph integral equations. This algorithm is an application of the matrix vector product approach in Galerkin formulation of the problem when the classical Jacobi polynomials are employed as natural basis functions. Our scheme has two main advantages. First, it produces a well-posed approximate method in the sense that the algebraic form of the Galerkin discretization of the problem has an upper triangular structure with a bounded condition number which can be solved directly by the forward substitution method and second, it has a potential convergence property such that its numerical error decay with the familiar spectral rate of convergence. Finally, some numerical examples are used to illustrate the efficiency and accuracy of the method.
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Mokhtary, P. Spectrally Accurate and Well-Posed Jacobi Galerkin Method for Multiple Delay Pantograph Integral Equations. Iran J Sci Technol Trans Sci 43, 959–967 (2019). https://doi.org/10.1007/s40995-017-0464-x
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DOI: https://doi.org/10.1007/s40995-017-0464-x
Keywords
- Galerkin method
- Jacobi polynomials
- Multiple delay pantograph integral equations
- Spectrally accurate
- Well posedness