Modified Laplace variational iteration method for solving fourth-order parabolic partial differential equation with variable coefficients

2019 ◽  
Vol 78 (6) ◽  
pp. 2052-2062 ◽  
Author(s):  
Muhammad Nadeem ◽  
Fengquan Li ◽  
Hijaz Ahmad
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

scholarly journals Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 33-46 ◽  
Author(s):  
Durgun Dogan ◽  
Ali Konuralp
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Data Set ◽  
Proportional Delays ◽  
Variational Iteration ◽  
Non Linear

In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

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