scholarly journals Convergence of Variational Iteration Method for Fractional Delay Integrodifferential-Algebraic Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yayun Fu ◽  
Hongliang Liu ◽  
Aiguo Xiao
Keyword(s):  
Iteration Method ◽  
Time Lag ◽  
Variational Iteration Method ◽  
Good Choice ◽  
Algebraic Equations ◽  
Science And Engineering ◽  
Variational Iteration ◽  
Fractional Delay ◽  
Restricted Variation ◽  
Algebraic Constraint

Fractional order delay integrodifferential-algebraic equations are often used for many practical modeling problems in science and engineering, which have time lag, memory, constraint limit, and so forth. These yield some difficulties in numerical computation. The iterative methods are good choice. In the present paper, we construct variational iteration method for solving them by using the appropriate restricted variation. This overcomes the difficulties caused by limitations of large storage amount and algebraic constraint and extends the previous conclusions.

scholarly journals On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Melike Karta ◽  
Ercan Çelik
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Variational Iteration

Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.

scholarly journals Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1642
Author(s):  
Ruyi Xing ◽  
Meng Liu ◽  
Kexin Meng ◽  
Shuli Mei
Keyword(s):  
Iteration Method ◽  
Exact Analytical Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Haar Wavelet ◽  
Algebraic Equations ◽  
Haar Wavelet Transform ◽  
Variational Iteration ◽  
Black Scholes Model ◽  
Black Scholes

Compared with the linear Black–Scholes model, nonlinear models are constructed through taking account of more practical factors, such as transaction cost, and so it is difficult to find an exact analytical solution. Combining the Haar wavelet integration method, which can transform the partial differential equation into the system of algebraic equations, the homotopy perturbation method, which can linearize the nonlinear problems, and the variational iteration method, which can solve the large system of algebraic equations efficiently, a novel numerical method for the nonlinear Black–Scholes model is proposed in this paper. Compared with the traditional methods, it has higher efficiency and calculation precision.

scholarly journals Comment on “A New Second-Order Iteration Method for Solving Nonlinear Equations”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Haibin Li
Keyword(s):  
Nonlinear Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Second Order ◽  
Algebraic Equations ◽  
Variational Iteration ◽  
Nonlinear Algebraic Equations ◽  
New Formulation

Kang et al. claimed that they obtained a new iteration formulation for nonlinear algebraic equations; however the “new” formulation was first derived in 2007 by the variational iteration method.

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