scholarly journals Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Umer Saeed ◽  
Mujeeb ur Rehman
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Quasilinearization Method ◽  
Nonlinear Boundary Value Problems ◽  
Wavelet Galerkin Method ◽  
Nonlinear Boundary Value ◽  
Quasilinearization Technique

A numerical method is proposed by wavelet-Galerkin and quasilinearization approach for nonlinear boundary value problems. Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. In each iteration of quasilinearization technique, solution is updated by wavelet-Galerkin method. In order to demonstrate the applicability of proposed method, we consider the various nonlinear boundary value problems.

scholarly journals Coupled System of Boundary Value Problems by Galerkin Method with Cubic B-Splines

2019 ◽  
Vol 128 ◽  
pp. 09008
Author(s):  
K.N.S Kasi Viswanadham
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Basis Functions ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering including heat and mass transfer. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a Galerkin method with cubic Bsplines as basis functions has been developed. The basis functions have been redefined into a new set of basis functions which vanish on the boundary. The nonlinear boundary value problems are solved with the help of quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

scholarly journals Modified Sinc-Galerkin Method for Nonlinear Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
M. A. Hajji ◽  
Q. M. Al-Mdallal
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Basis Functions ◽  
Accurate Approximation ◽  
Nonlinear Boundary Value Problems ◽  
Thomas Fermi ◽  
Nonlinear Boundary Value

This paper presents a modified Galerkin method based on sinc basis functions to numerically solve nonlinear boundary value problems. The modifications allow for the accurate approximation of the solution with accurate derivatives at the endpoints. The algorithm is applied to well-known problems: Bratu and Thomas-Fermi problems. Numerical results demonstrate the clear advantage of the suggested modifications in obtaining accurate numerical solutions as well as accurate derivatives at the endpoints.

scholarly journals Existence of solutions for fourth-order nonlinear boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mingzhu Huang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Lower Solution ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Quasilinearization Technique

AbstractIn this paper, we discuss the existence and approximation of solutions for a fourth-order nonlinear boundary value problem by using a quasilinearization technique. In the presence of a lower solution α and an upper solution β in the reverse order $\alpha \geq \beta $ α ≥ β , we show the existence of (extreme) solution.

scholarly journals On the extremal solution for a nonlinear boundary value problems of fractional p-Laplacian differential equation

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3771-3778 ◽  
Author(s):  
Youzheng Ding ◽  
Zhongli Wei
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Extremal Solution ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

This paper is concerned with the existence and uniqueness of extremal solution for a nonlinear boundary value problems of fractional differential equation involving Riemann-Liouville derivative and p-Laplacian operator. By applying monotone iterative technique and lower and upper solutions method, we obtain sufficient conditions for the existence and uniqueness of extremal solution and construct the sequences of iteration to approximate it. The paper extends the applications of lower and upper solutions method and obtains some new results.

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