An improved second-order numerical scheme for the Burgers-Fisher equation

2013 ◽  
Vol 54 ◽  
pp. 181
Author(s):  
Athanassios G. Bratsos
Keyword(s):  
Numerical Scheme ◽  
Second Order ◽  
Fisher Equation

A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation

2019 ◽  
Vol 57 (1) ◽  
pp. 495-525 ◽  
Author(s):  
Wenbin Chen ◽  
Xiaoming Wang ◽  
Yue Yan ◽  
Zhuying Zhang
Keyword(s):  
Numerical Scheme ◽  
Second Order ◽  
Hilliard Equation ◽  
Cahn Hilliard Equation

scholarly journals Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3050
Author(s):  
Sarita Nandal ◽  
Mahmoud A. Zaky ◽  
Rob H. De Staelen ◽  
Ahmed S. Hendy
Keyword(s):  
Fourth Order ◽  
Numerical Scheme ◽  
Source Term ◽  
Variable Coefficients ◽  
Second Order ◽  
Order Accuracy ◽  
Nonlinear Source ◽  
Second Order In Time ◽  
Convergence Orders ◽  
Temporal Direction

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 the L2−1σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

An Explicit Second-Order Numerical Scheme to Solve Decoupled Forward Backward Stochastic Equations

2014 ◽  
Vol 4 (4) ◽  
pp. 368-385 ◽  
Author(s):  
Yu Fu ◽  
Weidong Zhao
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
High Accuracy ◽  
Stochastic Equations ◽  
Explicit Scheme ◽  
Second Order ◽  
General Error

AbstractAn explicit numerical scheme is proposed for solving decoupled forward backward stochastic differential equations (FBSDE) represented in integral equation form. A general error inequality is derived for this numerical scheme, which also implies its stability. Error estimates are given based on this inequality, showing that the explicit scheme can be second-order. Some numerical experiments are carried out to illustrate the high accuracy of the proposed scheme.

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