scholarly journals Effective Boundary Value Problem Solver via Bézier Functions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 736
Author(s):  
Daegyun Choi ◽  
Henzeh Leeghim ◽  
Donghoon Kim
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Boundary Value ◽  
Initial Guess ◽  
Problem Solver ◽  
Spherically Symmetric ◽  
Initial Value ◽  
Effective Boundary

In engineering disciplines, many important problems are to be formed as boundary value problems (BVPs) that have conditions that are specified at the extremes. To handle such problems, the conventional shooting method that transforms BVPs into initial value problems has been extensively used, but it does not always guarantee solving the problem due to the possible failure of finding a proper initial guess. This paper proposes a universal initial guess finder that is composed of Bézier functions. Various dimensional problems that include Lambert’s problem for several orbits around the spherically symmetric Earth are studied to validate the efficacy of the proposed approach, and the results are compared.

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.

scholarly journals SOME ANALOGUES OF A THEOREM OF PEANO FOR BOUNDARY VALUE PROBLEM

1991 ◽  
Vol 22 (1) ◽  
pp. 83-98
Author(s):  
RICK BRANTLEY ◽  
JOHNNY HENDERSON
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Boundary Values ◽  
Initial Value ◽  
Boundary Points

Under certain conditions, solutions of boundary value problems for $y'''=f (x,y, y', y'')$ are differentiated with respect to boundary conditions, both boundary points and boundary values. The results obtained are analogues of one of Peano's theorems on initial value problems.

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.

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.

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