This report presents an experimental comparison of NAG Fortran Library software for the solution of large sparse unsymmetric linear systems of algebraic equations Preconditioned RGMRES CGS and Bi CGSTAB methods to be introduced at Mark are compared against one another and against direct methods Test problems include discrete approximations to D elliptic partial di erential equations random valu...

In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which ...

This report presents experimental results for new NAG Fortran Library software for the solution of large sparse symmetric linear systems of algebraic equations Preconditioned conjugate gradient methods introduced at Mark are compared against iterative and direct methods previously available in the library Test problems include discrete approximations to d elliptic partial di erential equations ...

Abstract: New physical principle for Monte-Carlo simulations has been introduced. It is based upon coupling of dynamical equations and the corresponding Liouville equation. The proposed approach does not require a random number generator since randomness is generated by instability of dynamics triggered and controlled by the feedback from the Liouville equation. Direct simulation of evolutionar...

The series solutions of the random nonlinear partial differential equations have been examined by a hybrid method. are studied both normal and uniform distributions. Two initial-value problems indicated to exemplify influence acquired Also, functions for first second moments approximate in MAPLE software. method is implemented analyze equations. software used find solutions. Besides, drawing fi...