An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations — Oak Academic Publishing
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An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations
Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA; Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt , Riyadh, KSA
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Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
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Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
1 Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA; Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt , Riyadh, KSA
2 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
3 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
In this paper, we propose and analyze some schemes of the integral collocation formulation based on Legendre polynomials. We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients. The properties of the Legendre polynomials are used to reduce the proposed problems to the solution of non-linear system of algebraic equations using Newton iteration method. We give numerical results to satisfy the accuracy and the applicability of the proposed schemes.
KeywordsIntegral Collocation FormulationSpectral MethodRiccatiLogistic and Delay Differential Equations
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