The general approach to chain equations derivation for the function generated by a Miura transformation analog is developing to account evolution (second Lax equation) and illustrated for Sturm-Liouville differential and difference operators. Polynomial differential operators case is investigated. Covariant sets of potentials are introduced by a periodic chain closure. The symmetry of the syste...

The series solution is widely applied to differential equations onR but is not found in q-differential equations. Applying the Taylor andmultiplication rule of two generalized polynomials, we develop a series solution of linear homogeneous q-difference equations. As an example, the series solution method is used to find a series solution of the second-order q-difference equation of Hermite’s type.

unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial differential equation.' this-equation cannot be solved analytically. hence, numerical methods. such as the finite element and the finite difference methods might be employed. in this study a mathematical model has been developed using the fully implicit finite difference method with control vol...

In this paper, based on the concept of domain decomposition and alternating group, we construct a class of Finite Difference method for fifth order dispersive equations, Stability Analysis for he method is given. Then we construct a new alternating group explicit iterative method. Both the two methods are suitable for parallel computation. Results of numerical experiments show the methods are e...

A novel general technique for treating electrically thin dispersive layer with the finite difference time domain (FDTD) method is introduced. The proposed model is based on the modifying of the node update equations to account for the layer, where the electric and magnetic flux densities are locally averaged in the FDTD grid. Then, based on the characteristics that the complex permittivity and ...

generally leads to a functional differential equation for f(x) and an associated inequality. It is only occasionally that the equation forf(x) reduces to a differential equation but it may sometimes reduce to a simple functional equation or difference equation. The analysis is easily extended by replacing the substitution z = x + r by some other substitution z = s(x) which transforms the range ...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...