Numeric‐analytical solution of an LC circuit with nonlinear capacitor based on the symplectic conservative perturbation method

2021 ◽  
Author(s):  
Hongwei Yang ◽  
Yingying Wang ◽  
Yuqi Wang ◽  
Fandi Lv
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Lc Circuit

Application of He’s Homotopy Perturbation Method to Stiff Systems of Ordinary Differential Equations

2008 ◽  
Vol 63 (1-2) ◽  
pp. 19-23 ◽  
Author(s):  
Mohammad Taghi Darvishi ◽  
Farzad Khani
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Stiff Systems ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear

We propose He’s homotopy perturbation method (HPM) to solve stiff systems of ordinary differential equations. This method is very simple to be implemented. HPM is employed to compute an approximation or analytical solution of the stiff systems of linear and nonlinear ordinary differential equations.

scholarly journals Verifying the Movable Elastoplastic Boundary Method by Using Galin’s Problem

2021 ◽  
Vol 2095 (1) ◽  
pp. 012087
Author(s):  
V.I. Bukhalov
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Biaxial Tension ◽  
Plastic Region ◽  
Elastoplastic Problem ◽  
Kirsch Problem ◽  
The World ◽  
Elastoplastic Region ◽  
Elastoplastic Boundary

Abstract Galin’s solution for the problem of biaxial tension of a plate with a hole completely covered by the plastic region appears to be a pearl recognized by the world scientific community. This solution serves as a test for all sorts of approximate approaches to solving elastoplastic problems, including the semi-analytical iterative method being developed by the author, focused on solving more complex problems such as the Kirsch problem in the elastoplastic formulation. The proposed iterative approach for a semi-analytical solution involves an explicit analytical expression for stresses in the plastic region and an iterative numerical solution in the elastic region with a refined border. The paper shows the convergence of the results based on the iterative procedure for the elastoplastic region boundary approaching its analytical position, which follows from the analytical solution of Galin’s elastoplastic problem. Consideration has also been given to obtaining results on the determination of the boundary between the elastic and plastic regions using a competing approximate perturbation method. The advantage of the proposed method lays in not limited modifications in parameters due to the requirement for small differences while formulating a problem from the axisymmetric case as seen in the perturbation method.

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