A SURVEY OF NUMERICAL METHODS FOR A NEW CLASS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ARISING IN NONSPHERICAL GEOMETRICAL OPTICS

1986 ◽  
pp. 257-263 ◽  
Author(s):  
Robert L. STERNBERG
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Geometrical Optics ◽  
Partial Differential ◽  
New Class

Application of New Triangular Functions to Nonlinear Partial Differential Equations

2009 ◽  
Vol 64 (1-2) ◽  
pp. 1-7 ◽  
Author(s):  
Emad A.-B. Abdel-Salam ◽  
Dogan Kaya
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Main Idea ◽  
Traveling Wave Solutions ◽  
Mkdv Equation ◽  
Kawahara Equation ◽  
Partial Differential ◽  
New Class ◽  
New Research

The results of some new research on a new class of triangular functions that unite the characteristics of the classical triangular functions are presented. Taking into consideration the great role played by triangular functions in geometry and physics, it is possible to expect that the new theory of the triangular functions will bring new results and interpretations in mathematics, biology, physics and cosmology. New traveling wave solutions of some nonlinear partial differential equations are obtained in a unified way. The main idea of this method is to express the solutions of these equations as a polynomial in the solution of the Riccati equation that satisfy the symmetrical triangular Fibonacci functions. We apply this method to the combined Korteweg-de Vries (KdV) and modified KdV (mKdV) equations, the generalized Kawahara equation, Ito’s 5th-order mKdV equation and Ito’s 7th-order mKdV equation.

scholarly journals A REVIEW ON NUMERICAL METHODS FOR NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 23 (07) ◽  
pp. 1342-1352
Author(s):  
◽  
Dr. Jatinder kaur ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Wave Equations ◽  
Numerical Models ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Non Linear ◽  
Linear Differential

Progression in innovation and engineering presents us with numerous difficulties, comparably to conquer such engineering difficulties with the assistance of various numerical models, equations are taken. Since in the first place Mathematicians, Designers and Engineers make progress toward accuracy what’s more, exactness while addressing equations Differential equations, specifically, hold an enormous application in engineering and numerous different areas. One such sort of Differential equation is known as partial differential equation. The range of application of partial differential equations comprises of recreation, calculation age, and investigation of higher request PDE and wave equations. Adjusting diverse numerical methods prompts an assortment of answers and contrast among them, subsequently the determination of the method of addressing is one of the urgent boundaries to produce exact outcomes. Our work centres’ around the survey of various numerical methods to settle Non-linear differential equations based on exactness and effectiveness, in order to diminish the emphases. These would orchestrate rules to existing numerical methods of nonlinear partial differential equations.[1]

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