in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for fractional diffusion equation. We also show stability convergence analysis fully discrete scheme a Crank–Nicolson time. A Black–Scholes equation is proposed tested numerically. Some numerical experiments are carried out to confirm a...

If T⃗ denotes a vector tangent to C at t,x,u then the direction numbers of T⃗ must be a,b, f. But then (1.2) implies that T⃗ n⃗, which is to say, T⃗ lies in the tangent plane to the surface S. But if T⃗ lies in the tangent plane, then C must lie in S. Evidently, solution curves of (1.2) lie in the solution surface S associated with (1.2). Such curves are called characteristic curves for (1.2). W...

2 Separation of variables and the complete integral 5 2.1 Separation of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The envelope of a family of curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The complete integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Determining the characteristic strips from t...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...