An Error Estimation Technique for the Solution of Ordinary Differential Equations in Chebyshev Series

Error Estimation for Collocation Solution of Linear Ordinary Differential Equations

This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of the residual rather than just its norm.

FUZZY INTEGRO-DIFFERENTIAL EQUATIONS: DISCRETE SOLUTION AND ERROR ESTIMATION

This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

A fractional type of the Chebyshev polynomials for approximation of solution of linear fractional differential equations

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

fuzzy integro-differential equations: discrete solution and error estimation

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

An Opertional Method for The Numerical Solution of Two Dimensional Linear Fredholm Integral Equations With an Error Estimation