Numerical Solution of Differential Equations by Direct Taylor Expansion

Numerical solution of Voltra algebraic integral equations by Taylor expansion method

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

NUMERICAL SOLUTION OF THE MOST GENERAL NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL-DIFFERENCE EQUATIONS BY USING TAYLOR POLYNOMIAL APPROACH

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

Approximate solution of fractional integro-differential equations by Taylor expansion method

Approximate solution of linear integro-differential equations by using modified Taylor expansion method

Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

Numerical Solution of Differential Equations