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.

scholarly journals An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
D. D. Ganji ◽  
Abbas Tahmasebi Poor
Keyword(s):  
Fluid Mechanics ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Iteration Method ◽  
Structural Engineering ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Variational Iteration Method ◽  
Nonlinear Boundary Value Problems ◽  
Linear And Nonlinear

Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.

scholarly journals Boundary value problems for differential equations with reflection of the argument

1985 ◽  
Vol 8 (1) ◽  
pp. 151-163 ◽  
Author(s):  
Joseph Wiener ◽  
A. R. Aftabizadeh
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Linear And Nonlinear

Linear and nonlinear boundary value problems for differential equations with reflection of the argument are considered.

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.

The generalized fractional order of the Chebyshev functions on nonlinear boundary value problems in the semi-infinite domain

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
Kourosh Parand ◽  
Mehdi Delkhosh
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Fractional Order ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Numerical Results ◽  
Algebraic Equations ◽  
Nonlinear Boundary Value Problems ◽  
Infinite Domain ◽  
Nonlinear Boundary Value

AbstractA new collocation method, namely the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) collocation method, is given for solving some nonlinear boundary value problems in the semi-infinite domain, such as equations of the unsteady isothermal flow of a gas, the third grade fluid, the Blasius, and the field equation determining the vortex profile. The method reduces the solution of the problem to the solution of a nonlinear system of algebraic equations. To illustrate the reliability of the method, the numerical results of the present method are compared with several numerical results.

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.

Sign in / Sign up

Export Citation Format

Share Document