High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations

High-Order Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations

A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space d...

The Stability of Non-standard Finite Difference Scheme for Solution of Partial Differential Equations of Fractional Order

Fractional derivatives and integrals are new concepts of derivatives and integrals of arbitrary order. Partial differential equations whose derivatives can be of fractional order are called fractional partial differential equations (FPDEs). Recently, these equations have received special attention due to their high practical applications. In this paper, we survey a rather general case of FPDE t...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

numerical solution of incompressible boussinesq equations using fourth-order compact scheme: lock exchange flow

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...