Algebraic Method for Group Classification of (1+1)-Dimensional Linear Schrödinger Equations

A Linear Algebra Method for Solving Systems of Algebraic Equations

We consider the exact computation of matrix eigenproblems in residue class rings for solving systems of algebraic equations. We construct multiplication tables using a Gröbner basis of a zero-dimensional ideal. Then, we analyze the tables by exactly computing their Frobenius normal forms. The derogatoriness and the diagonalizability are determined by the normal forms, and the problem is divided...

A Modified Newton Method for Solving Non-linear Algebraic Equations

The Newton algorithm based on the “continuation” method may be written as being governed by the equation ( ) j x t + 1 ( ) 0, ij i j B F x − = where Fi (xj) = 0, i, j = 1, ...n are nonlinear algebraic equations (NAEs) to be solved, and Bij = ∂Fi /∂xj is the corresponding Jacobian matrix. It is known that the Newton’s algorithm is quadratically convergent; however, it has some drawbacks, such as...

A Modified Chord Newton’s Method for High-dimensional Algebraic Equations

There is a great deal of interest on reducing overall computational budget of classical Newton’s method for solving nonlinear systems of equations. The appealing approach is based on chord Newton’s but the method mostly requires high number of iteration as the dimension of the systems increases. In this paper, we introduce a new procedure that will reduce the well known shortcoming of Newton me...

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

Analysis of Linear Two-Dimensional Equations by Hermitian Meshfree Collocation Method

Meshfree Collocation Method is used to solve linear two-dimensional problems. This method differs from weak form methods such as Galerkin method and no cellular networking and no numerical  integration. Therefore, this method has no constraints such as the integration accuracy and the integration CPU time, and equations can be isolated directly from the strong form of governing PDE. The fundame...