Adomian decomposition method, as a convenience device has been used to solve many functional equations so far. In this manuscript, we consider a system of nonlinear ordinary differential equations, which governs on general reaction in biochemistry as a theoretical problem of concentration kinetics. These system, which is known as Brusselator system has been solved by applying Adomian decomposit...

Conceptual graphs are both a language for representing knowledge and patterns for constructing models. They form models in the AI sense of structures that approximate some actual or possible system in the real world. They also form models in the logical sense of structures for which some set of axioms are true. When combined with recent developments in nonstandard logic and semantics, conceptua...

We discuss a new approach to represent fractional operators by Sinc approximation using convolution integrals. A spin off of the convolution representation is an effective inverse Laplace transform. Several examples demonstrate the application of the method to different practical problems.

Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary convection-diffusion equations, which are based on use of new variables. Also, we consider these equations in the form of convection-diffusion-reaction and constru...

The present paper develops a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given by a Runge-Kutta process. These NCEs are defined in such a way that the continuous solutions furnished by the one-step collocation methods are included.

For semidiscrete approximations and one-step fully discretized approximations of the initial-boundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or l2 stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable...