Optimal solution for Koper-Schmidt equation using Jacobi and Airfoil expansion methods

Subject Areas : Statistics

shadan sadigh behzadi ¹ , F. Gervehei ² , A. Rafie ³

1 - Department of Mathematics, Islamic Azad University,Qazvin Branch,Qazvin,Iran.
2 - Department of Mathematics, Islamic Azad University,Qazvin Branch,Qazvin,Iran.
3 - Department of Mathematics, Islamic Azad University,Qazvin Branch,Qazvin,Iran

Received: 2019-12-24 Accepted : 2021-05-30 Published : 2021-07-23

Keywords: پایه متعامد ایرفویل, روش هم محلی, پایه متعامد ژاکوپی, معادله ی کوپر-اشمیت,

Abstract :

In this paper, we solve the Cooper-Schmidt equation in a way that is consistent with Jacuzzi and Airfoil foundations. This PDE equation is one of the most important equations in physics and chemistry. This nonlinear equation in mechanical engineering appears as a wave phenomenon, and in plasma physics discusses systems that are composed of positive and negative charged particles that can move freely. Comparison of the level of hot electron production and its surface causes the harmonic emission of some source signals and the heat electrons in the plasma are radiated spherically [1]. The Cooper-Schmidt equation plays an important role in nonlinear wave scattering. Individual waves are propagated in the nonlinear scattering of media. These waves maintain a stable shape. Due to the dynamic equilibrium and nonlinearity of this equation, an approximate solution has been proposed in many papers [12, 13]. In this paper, by applying numerical methods to the desired equation, nonlinear devices can be obtained that can be obtained by the method. Solved nonlinear systems, such as Newton's iterative method. The existence, uniqueness of the answer, and convergence of methods are examined.

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