Solving Differential-algebraic Equations by Taylor Series (i): Computing Taylor Coefficients
نویسندگان
چکیده
This paper is one of a series underpinning the authors’ DAETS code for solving DAE initial value problems by Taylor series expansion. First, building on the second author’s structural analysis of DAEs (BIT 41 (2001) 364–394), it describes and justifies the method used in DAETS to compute Taylor coefficients (TCs) using automatic differentiation. The DAE may be fully implicit, nonlinear, and contain derivatives of order higher than one. Algorithmic details are given. Second, it proves that either the method succeeds in the sense of computing TCs of the local solution, or one of a number of detectable error conditions occurs. AMS subject classification: 34A09, 65L80, 65L05, 41A58.
منابع مشابه
Solving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.
متن کاملNUMERICAL 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 ...
متن کاملAn Approximate Method for System of Nonlinear Volterra Integro-Differential Equations with Variable Coefficients
In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...
متن کاملThe combined reproducing kernel method and Taylor series for solving nonlinear Volterra-Fredholm integro-differential equations
In this letter, the numerical scheme of nonlinear Volterra-Fredholm integro-differential equations is proposed in a reproducing kernel Hilbert space (RKHS). The method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. The nonlinear terms are replaced by its Taylor series. In this technique, the nonlinear Volterra-Fredholm integro...
متن کاملThe Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
This paper presents the numerical solution for a class of fractional differential equations. The fractional derivatives are described in the Caputo cite{1} sense. We developed a reproducing kernel method (RKM) to solve fractional differential equations in reproducing kernel Hilbert space. This method cannot be used directly to solve these equations, so an equivalent transformation is made by u...
متن کامل