This article focuses on the approximation of conventional second order derivative via the combined (diamond-α) dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates t...

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using L2?1? approximation time Caputo derivative, finite difference method second-order accuracy in temporal direction achieved. novelty introduce problem under consideration coefficients, nonlinear source term, delay constant. re...

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

The aim of this work is to provide the first strong convergence result numerical approximation a general time-fractional second order stochastic partial differential equation involving Caputo derivative in time $\alpha\in(\frac 12; 1)$ and driven simultaneously by multiplicative standard Brownian motion additive fBm with Hurst parameter $H\in(\frac 12, 1)$, more realistic model random effects o...

I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy effective theory is solved using the strong coupling expansion. In some models there exists an intermediate scale at which both expansions make sense. The method is...