In this paper, we propose a method to approximate the solution of a linear Fredholm integro-differential equation by using the Chebyshev wavelet of the first kind as basis. For this purpose, we introduce the first Chebyshev operational matrix of integration. Chebyshev wavelet approximating method is then utilized to reduce the integro-differential equation to a system of algebraic equations. Il...

Nonsmooth equation-solving and optimization algorithms which require local sensitivity information are extended to systems with nonsmooth parametric differential-algebraic equations embedded. Nonsmooth differential-algebraic equations refers here to semi-explicit differential-algebraic equations with algebraic equations satisfying local Lipschitz continuity and differential right-hand side func...

In this paper, Numerical solution of Differential-Algebraic equations (DAEs) with index-3 is considered by Pade approximation. We applied this method to two examples. First differential-algebraic equations (DAEs) with index-3 has been converted to power series by one-dimensional differential transformation, Then the numerical solution of equation was put into Pade series form. Thus we obtained ...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...