scholarly journals Symplectic multiquadric quasi-interpolation approximations of KdV equation

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5161-5171
Author(s):  
Shengliang Zhang ◽  
Liping Zhang
Keyword(s):  
Kdv Equation ◽  
Order Approximation ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Approximation Properties ◽  
High Order Approximation ◽  
Shape Preserving ◽  
Order Accuracy ◽  
Long Time

Radial basis functions quasi-interpolation is very useful tool for the numerical solution of differential equations, since it possesses shape-preserving and high-order approximation properties. Based on multiquadric quasi-interpolations, this study suggests a meshless symplectic procedure for KdV equation. The method has a number of advantages over existing approaches including no need to solve a resultant full matrix, accuracy and ease of implementation. We also present a theoretical framework to show the conservativeness and convergence of the proposed method. As the numerical experiments show, it not only offers a high order accuracy but also has a good property of long-time tracking capability.

High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II)

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Jianxiong Cao ◽  
Changpin Li ◽  
YangQuan Chen
Keyword(s):  
Dirichlet Boundary ◽  
Order Approximation ◽  
High Order ◽  
Dirichlet Boundary Conditions ◽  
High Order Accuracy ◽  
High Order Approximation ◽  
Order Accuracy ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
New Formula

AbstractIn this paper, we first establish a high-order numerical algorithm for α-th (0 < α < 1) order Caputo derivative of a given function f(t), where the convergence rate is (4 − α)-th order. Then by using this new formula, an improved difference scheme with high order accuracy in time to solve Caputo-type fractional advection-diffusion equation with Dirichlet boundary conditions is constructed. Finally, numerical examples are carried out to confirm the efficiency of the constructed algorithm.

Convergence of a highly accurate quasi-interpolation method for options pricing

2017 ◽  
Vol 04 (04) ◽  
pp. 1750048
Author(s):  
Shengliang Zhang
Keyword(s):  
Stock Price ◽  
Interpolation Method ◽  
High Order ◽  
Basis Functions ◽  
High Order Accuracy ◽  
Options Pricing ◽  
Interpolation Scheme ◽  
Time Step ◽  
Order Accuracy ◽  
Tree Approach

A highly accurate radial basis functions (RBFs) quasi-interpolation method for calculating American options prices has been presented by some researchers, which possesses a high order accuracy compared with existing numerical methods. In this study, we show the convergence of the proposed RBFs quasi-interpolation scheme from the view point of probability. It will be confirmed to be a multinomial tree approach, in which in one time step the underlying stock price can arrive at an infinity of possible values. This helps understand the high-order accuracy of the method.

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

2016 ◽  
Vol 9 (4) ◽  
pp. 619-639 ◽  
Author(s):  
Zhong-Qing Wang ◽  
Jun Mu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
High Order Accuracy ◽  
Nonlinear Ordinary Differential Equations ◽  
Initial Value ◽  
Order Accuracy ◽  
Long Time

AbstractWe introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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