this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...

We formulate a quasilinear parabolic equation describing the behavior of global-in-time solution to semilinear equation. study this in accordance with blow-up and quenching patterns original This is new theory partial differential equations presents several difficulties for mathematical analysis. Two approaches are examined: functional analysis viscosity solution.

This paper is concerned with the numerical solution of parabolic equations coupled to gradient equations. The gradient equations are ordinary diierential equations whose solutions deene positions of particles in the spatial domain of the parabolic equations. The vector eld of the gradient equations is determined by gradients of solutions to the parabolic equations. Such mixed parabolic-gradient...

This work introduces a new operator-splitting method for solving the two-dimensional (2D) and three-dimensional (3D) parabolic equations. The aim is to reduce the computational complexity without loss of accuracy. Firstly, we split the 2D and 3D parabolic equations into a sequence of one-dimensional (1D) parabolic equations respectively, then we solve each 1D parabolic equation by using finite ...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.