Numerical Methods for Nonlinear Partial Differential Equations

Author(s):  
Sören Bartels
2021 ◽  
Vol 23 (07) ◽  
pp. 1342-1352
Author(s):  
◽  
Dr. Jatinder kaur ◽  

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]


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.


Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 545-554
Author(s):  
Asghar Ali ◽  
Aly R. Seadawy ◽  
Dumitru Baleanu

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.


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