Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

In this work, we present the numerical solution of fractional order Volterra–Fredholm integro-differential equations using the second kind of Chebyshev collocation technique. First, we transformed the problem into a system of linear algebraic equations, which are then solved using matrix inversion to obtain the unknown constants. Furthermore, numerical examples are used to outline the method’s accuracy and efficiency using tables and figures. The results show that the method performed better in terms of improving accuracy and requiring less rigorous work.©2022 JNSMR UIN Walisongo. All rights reserved

Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

In this work, we present the numerical solution of fractional order Volterra–Fredholm integro-differential equations using the second kind of Chebyshev collocation technique. First, we transformed the problem into a system of linear algebraic equations, which are then solved using matrix inversion to obtain the unknown constants. Furthermore, numerical examples are used to outline the method’s accuracy and efficiency using tables and figures. The results show that the method performed better in terms of improving accuracy and requiring less rigorous work.©2022 JNSMR UIN Walisongo. All rights reserved

Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

In this work, we present the numerical solution of fractional order Volterra–Fredholm integro-differential equations using the second kind of Chebyshev collocation technique. First, we transformed the problem into a system of linear algebraic equations, which are then solved using matrix inversion to obtain the unknown constants. Furthermore, numerical examples are used to outline the method’s accuracy and efficiency using tables and figures. The results show that the method performed better in terms of improving accuracy and requiring less rigorous work.©2022 JNSMR UIN Walisongo. All rights reserved

Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations

This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE

Numerical Solutions for Linear Fredholm Integro-Differential Difference Equations with Variable Coefficients by Collocation Methods

We employed an efficient numerical collocation approximation methods to obtain an approximate solution of linear Fredholm integro-differential difference equation with variable coefficients. An assumed approximate solutions for both collocation approximation methods are substituted into the problem considered. After simplifications and collocations, resulted into system of linear algebraic equations which are then solved using MAPLE 18 modules to obtain the unknown constants involved in the assumed solution. The known constants are then substituted back into the assumed approximate solution. Numerical examples were solved to illustrate the reliability, accuracy and efficiency of these methods on problems considered by comparing the numerical solutions obtained with the exact solution and also with some other existing methods. We observed from the results obtained that the methods are reliable, accurate, fast, simple to apply and less computational which makes the valid for the classes of problems considered.   Keywords: Approximate solution, Collocation, Fredholm, Integro-differential difference and linear algebraic equation