Discrete cubic spline technique for solving one-dimensional Bratu’s problem

2021 ◽  
pp. 2250011
Author(s):  
Pooja Khandelwal ◽  
Arshad Khan ◽  
Talat Sultana
Keyword(s):  
Boundary Value Problems ◽  
Convergence Analysis ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Cubic Spline ◽  
Spline Method ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Bratu’S Problem ◽  
Highly Nonlinear

In this paper, discrete cubic spline method based on central differences is developed to solve one-dimensional (1D) Bratu’s and Bratu’s type highly nonlinear boundary value problems (BVPs). Convergence analysis is briefly discussed. Four examples are given to justify the presented method and comparisons are made to confirm the advantage of the proposed technique.

scholarly journals Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ishfaq Ahmad Ganaie ◽  
Shelly Arora ◽  
V. K. Kukreja
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Spline Method ◽  
Orthogonal Collocation ◽  
Nonlinear Boundary Value Problems ◽  
B Spline ◽  
Linear And Nonlinear ◽  
Volume Method

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

2013 ◽  
Vol 24 (11) ◽  
pp. 1350082 ◽  
Author(s):  
RAFAEL G. CAMPOS ◽  
RAFAEL GARCÍA RUIZ
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Kdv Equation ◽  
Boundary Value ◽  
Soliton Solutions ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Dimensional Boundary ◽  
The Fourier Transform ◽  
Derivatives Of

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

scholarly journals Nonlinear boundary value problems for elliptic systems

1987 ◽  
Vol 30 (2) ◽  
pp. 257-272 ◽  
Author(s):  
A. Cañada
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Dimensional Space ◽  
Boundary Value ◽  
Elliptic Systems ◽  
First Eigenvalue ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Negative Function ◽  
Image Position

The purpose of this paper is to discuss non-linear boundary value problems for elliptic systems of the typewhere Ak is a second order uniformly elliptic operator and is such that the problemhas a one-dimensional space of solutions that is generated by a non-negative function. The boundary ∂G is supposed to be smooth and the functions gk, 1≦k≦m are defined on Ḡ×Rm and are continuously differentiate (usually, Bk represents Dirichlet or Neumann conditions and is the first eigenvalue associated with Ak and such boundary conditions).

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