scholarly journals Recent Advances in the Study of a Fourth-Order Compact Scheme for the One-Dimensional Biharmonic Equation

2012 ◽  
Vol 53 (1) ◽  
pp. 55-79 ◽  
Author(s):  
D. Fishelov ◽  
M. Ben-Artzi ◽  
J.-P. Croisille
Keyword(s):  
Fourth Order ◽  
Biharmonic Equation ◽  
Compact Scheme ◽  
One Dimensional ◽  
Recent Advances ◽  
Fourth Order Compact Scheme ◽  
The One

scholarly journals Time-Compact Scheme for the One-Dimensional Dirac Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Jun-Jie Cao ◽  
Xiang-Gui Li ◽  
Jing-Liang Qiu ◽  
Jing-Jing Zhang
Keyword(s):  
Dirac Equation ◽  
Fourth Order ◽  
Compact Scheme ◽  
Order Accuracy ◽  
Spectral Order ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
One Dimensional ◽  
The One ◽  
Discrete Charge

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.

FOURTH-ORDER COMPACT SCHEME FOR OPTION PRICING UNDER THE MERTON’S AND KOU’S JUMP-DIFFUSION MODELS

2018 ◽  
Vol 21 (04) ◽  
pp. 1850027 ◽  
Author(s):  
KULDIP SINGH PATEL ◽  
MANI MEHRA
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Linear Equations ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
Compact Scheme ◽  
Discrete Problem ◽  
Option Prices ◽  
Fully Discrete ◽  
Fourth Order Compact Scheme

In this paper, a compact scheme with three time levels is proposed to solve the partial integro-differential equation that governs the option prices in jump-diffusion models. In the proposed compact scheme, the second derivative approximation of the unknowns is approximated using the value of these unknowns and their first derivative approximations, thereby allowing us to obtain a tridiagonal system of linear equations for a fully discrete problem. Moreover, the consistency and stability of the proposed compact scheme are proved. Owing to the low regularity of typical initial conditions, a smoothing operator is employed to ensure the fourth-order convergence rate. Numerical illustrations concerning the pricing of European options under the Merton’s and Kou’s jump-diffusion models are presented to validate the theoretical results.

scholarly journals Fourth-Order Deferred Correction Scheme for Solving Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Yambangwai ◽  
N. P. Moshkin
Keyword(s):  
Fourth Order ◽  
Heat Conduction Problem ◽  
Correction Method ◽  
Dirichlet Boundary Conditions ◽  
Heat Conducting ◽  
One Dimensional ◽  
Deferred Correction ◽  
The Stability ◽  
The One ◽  
Nicolson Scheme

A deferred correction method is utilized to increase the order of spatial accuracy of the Crank-Nicolson scheme for the numerical solution of the one-dimensional heat equation. The fourth-order methods proposed are the easier development and can be solved by using Thomas algorithms. The stability analysis and numerical experiments have been limited to one-dimensional heat-conducting problems with Dirichlet boundary conditions and initial data.

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