NUMERICAL SOLUTION FOR SOLVING THE QUADRATIC RICCATI DIFFERENTIAL EQUATIONS BY MULTISTAGE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD

2017 ◽  
Vol 101 (4) ◽  
pp. 839-853
Author(s):  
N. R. Anakira
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Riccati Differential Equations ◽  
Optimal Homotopy Asymptotic Method

scholarly journals A Semi-Analytical Solution of Thick Truncated Cones Using Matched Asymptotic Method and Disk Form Multilayers

2014 ◽  
Vol 61 (3) ◽  
pp. 495-513 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Finite Element Method ◽  
Shear Stress ◽  
Analytical Solution ◽  
Differential Equations ◽  
Numerical Solution ◽  
Asymptotic Method ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Truncated Cone

Abstract In this article, the thick truncated cone shell is divided into disk-layers form with their thickness corresponding to the thickness of the cone. Due to the existence of shear stress in the truncated cone, the equations governing disk layers are obtained based on first shear deformation theory. These equations are in the form of a set of general differential equations. Given that the truncated cone is divided into n disks, n sets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The results obtained have been compared with those obtained through the analytical solution and the numerical solution. For the purpose of the analytical solution, use has been made of matched asymptotic method (MAM) and for the numerical solution, the finite element method (FEM).

scholarly journals Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

2018 ◽  
Vol 148 ◽  
pp. 13003 ◽  
Author(s):  
Nicolae Herisanu ◽  
Vasile Marinca
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Approximate Method ◽  
Excellent Agreement ◽  
Electrostatic Field ◽  
Asymptotic Method ◽  
Integro Differential Equation ◽  
Analytical Results ◽  
Post Buckling ◽  
Optimal Homotopy Asymptotic Method

In the present paper, the post-buckling response of an axially stressed clamped-clamped actuator, modeled as a beam and subjected to a symmetric electrostatic field is analyzed. An analytical approximate method, namely the Optimal Homotopy Asymptotic Method (OHAM) is applied to the governing nonlinear integro-differential equation. The analytical results obtained through the proposed procedure show excellent agreement with numerical solution, proving the validity of the proposed procedure, which is simple and easy to use.

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