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 ...

An effective method based upon Alpert multiwavelets is proposed for the solution of Hallen’s integral equation. The properties of Alpert multiwavelets are first given. These wavelets are utilized to reduce the solution of Hallen’s integral equation to the solution of sparse algebraic equations. In order to save memory requirement and computation time, a threshold procedure is applied to obtain ...

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

Implicit time-step numerical integrators for ordinary and evolutionary partial di erential equations need, at each step, the solution of linear algebraic equations that are unsymmetric and often large and sparse. Recently, a block preconditioner based on circulant approximations for the linear systems arising in the boundary value methods (BVMs) was introduced by the author. Here, some circulan...

Abstract. The main purpose of this article is to present an approximate solution for the one dimensional wave equation subject to an integral conservation condition in terms of second kind Chebyshev polynomials. The operational matrices of integration and derivation are introduced and utilized to reduce the wave equation and the conditions into the matrix equations which correspond to a system ...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

The bosonic large-[Formula: see text] master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. task is then calculate this as a solution master-field equation. We consider simplified version algebraic equation and take dimensionality [Formula: size text]. For explicit realization pseudorandom constants entering equation, we establish existence find, ...

A new algorithm is proposed for obtaining explicit solutions of the Cauchy problem defined by a certain class of partial differential equations (PDE) of parabolic type. The algorithm exploits the algebraic structure of the problem to transform the PDE into an ordinary matrix differential equation, which is then solved by Lie algebraic techniques.

The initial value problem for a matrix Riccati differential equation associated with an M -matrix is known to have a global solution X(t) on [0,∞) when X(0) takes values from a suitable set of nonnegative matrices. It is also known, except for the critical case, that as t goes to infinity X(t) converges to the minimal nonnegative solution of the corresponding algebraic Riccati equation. In this...