Symbolic Computation on Complex Polynomial Solution of Differential Equations

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 ...

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

Tau Numerical Solution of Volterra Integro-Differential Equations With Arbitrary Polynomial Bases

Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations

We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar...

Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations

A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm determines the conditions on the parameters so that the equations might admit polynomial solutions in tanh. Examples illustrate the key steps of the algorithm. Parallels are drawn through discussion and example to the tan...