A note on the transformation of boundary value problems to initial value problems: The iterative transformation method

2022 ◽  
Vol 415 ◽  
pp. 126692
Author(s):  
A.G. Fareo
Keyword(s):  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Transformation Method ◽  
Initial Value

scholarly journals Spectral approximations to the fractional integral and derivative

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Changpin Li ◽  
Fanhai Zeng ◽  
Fawang Liu
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Caputo Derivative ◽  
Initial Value Problems ◽  
Fractional Integral ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
Initial Value ◽  
Numerical Examples ◽  
Spectral Approximations

AbstractIn this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

On the Connection between Statical and Dynamical Chaos

1989 ◽  
Vol 44 (7) ◽  
pp. 645-650 ◽  
Author(s):  
M. S. El Naschie ◽  
S. Al Athel
Keyword(s):  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Dynamical Chaos ◽  
Initial Value ◽  
Elastic Systems

The paper discusses the interrelationship between statical chaos and dynamical initial value problems. It is pointed out that approximate homoclinic and heteroclinic solitons can be perturbed to produce spacial asymptotic chaos in some buckled structural elastic systems which constitute strictly speaking boundary value problems.

scholarly journals An Intial-Value Technique for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems

2020 ◽  
Vol 25 (1) ◽  
pp. 106-126
Author(s):  
P. Padmaja ◽  
P. Aparna ◽  
R.S.R. Gorla
Keyword(s):  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Original Problem ◽  
Boundary Value ◽  
Point Of View ◽  
Singularly Perturbed ◽  
Initial Value ◽  
Computational Point ◽  
First Order ◽  
Runge Kutta Method

AbstractIn this paper, we present an initial value technique for solving self-adjoint singularly perturbed linear boundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and right-end layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.

Sign in / Sign up

Export Citation Format

Share Document