A Novel Spectral Modified Pell Polynomials for Solving Singular Differential Equations
Autor: | Suha Shihab, Mohammed Abdelhadi Sarhan, Mohammed Rasheed |
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Rok vydání: | 2021 |
Předmět: |
singular initial value problem
Differential equation modified pell polynomials Science Mathematics::Number Theory Mathematics::History and Overview spectral method Derivative product matrix of two modified pell polynomials Operational matrix Scheme (mathematics) Product (mathematics) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Exact formula Initial value problem Applied mathematics operation matrix Spectral method Earth-Surface Processes Mathematics |
Zdroj: | Mustansiriyah Journal of Science, Vol 32, Iss 1, Pp 18-24 (2021) |
ISSN: | 2521-3520 1814-635X |
Popis: | This paper studies the modified Pell polynomials. Some important properties of modified Pell polynomials are presented. An exact formula of modified Pell polynomials derivative in terms of modified Pell themselves is first derived with the proof and then a new relationship is constructed which relates the modified Pell polynomials expansion coefficients of a derivative in terms of their original expansion coefficients. An interesting new formula for the product operational matrix of modified Pell polynomials is also derived in this work. With modified Pell polynomials expansion scheme, the powers 1, x, …, xn are expressed in terms of such polynomials. The main goal of all presented formulas is to simplify the original equations and the determination of the coefficients of expansion based on modified Pell polynomials will be easy. Spectral techniques together with all the derived formulas of modified Pell polynomials are utilized to solve some singular initial value problems. Three test examples are solved in this work to illustrate the validity of the proposed method. The computational method is replaced by exact and explicit formulas. More accurate results are obtained than those presented by other existing methods in the literature. |
Databáze: | OpenAIRE |
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