Block eigenvalues and solutions of differential matrix equations

Efficient Solutions of Coupled Matrix and Matrix Differential Equations

In Kronecker products works, matrices are some times regarded as vectors and vectors are some times made in to matrices. To be precise about these reshaping we use the vector and diagonal extraction operators. In the present paper, the results are organized in the following ways. First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this prob...

Using operational matrix for numerical solution of fractional differential equations

In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. The method provides the solution in the form of a rapidly convergent series. Furthermore, error analysis of the pro...

Computing eigenvalues of ordinary differential equations

Discretisations of differential eigenvalue problems have a sensitivity to perturbations which is asymptotically least as h→ 0 when the differential equation is in first order system form. Both second and fourth order accurate discretisations of the first order system are straightforward to derive and lead to generalised eigenvalue problems of the form (A(h)− λB(h))v = 0 , where both A and B are...

Application of the block backward differential formula for numerical solution of Volterra integro-differential equations

In this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability r...

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations