Iterative solutions for a beam equation with nonlinear boundary conditions of third order

Fu, To; Silva, Jair Da

doi:10.1016/j.amc.2003.08.088

Cited by 70 publications

(62 citation statements)

References 7 publications

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“…The integration constants c 1 , c 2 , c 3 , c 4 are evaluated using the boundary conditions (2). It is observed that c 4 is equal to zero because of the boundary condition w(0) ¼ 0.…”

Section: Successive Approximation Methodsmentioning

confidence: 99%

Iterative algorithms for optimal design of columns subject to a stress constraint

Adali

Cagdas

2007

Journal of the Franklin Institute

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“…The integration constants c 1 , c 2 , c 3 , c 4 are evaluated using the boundary conditions (2). It is observed that c 4 is equal to zero because of the boundary condition w(0) ¼ 0.…”

Section: Successive Approximation Methodsmentioning

confidence: 99%

Iterative algorithms for optimal design of columns subject to a stress constraint

Adali

Cagdas

2007

Journal of the Franklin Institute

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“…(15)- (18), along with the given boundary conditions and the power series expansion of y in Eq. (8) and collecting coefficients of similar powers of ξ, yield the following equation…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Consider the following boundary value problem involving nonlinear boundary conditions which appears in the study of deformations of elastic beams on elastic bearings [8,9]:…”

Section: Example 2 Consider the Following Fourth Order Differential mentioning

confidence: 99%

“…(8). Equations (8) and (9) provide the solution and its derivative at any domain point in terms of the boundary values and the forcing function P and therefore, called the domain integral equations.…”

Section: Integral Equationsmentioning

confidence: 99%

“…(1) is cast in an integral form (Eqs. (8), (9) and (10)). Then, the integral equations (8), (9) and (10) are solved by expressing the dependent variable y as a power series, the coefficients of which can be obtained by equating the terms of similar powers.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Boundary integral solution for a class of fourth-order two-point boundary value problems

Al-Gahtani

2016

J. Appl. Math. Comput. Mech.

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Abstract. In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation, ‫ܮ‬ሻ, where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.

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A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space

Yang

Cui

2010

Math. Meth. Appl. Sci.

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In this paper, a new numerical algorithm is provided to solve nonlinear multi-point boundary value problems in a very favorable reproducing kernel space, which satisfies all complex boundary conditions. Its reproducing kernel function is discussed in detail. The theorem proves that the approximate solution and its first-and second-order derivatives all converge uniformly. The numerical experiments show that the algorithm is quite accurate and efficient for solving nonlinear multi-point boundary value problems.

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Iterative solutions for a beam equation with nonlinear boundary conditions of third order

Cited by 70 publications

References 7 publications

Iterative algorithms for optimal design of columns subject to a stress constraint

Iterative algorithms for optimal design of columns subject to a stress constraint

Boundary integral solution for a class of fourth-order two-point boundary value problems

A numerical solution to nonlinear multi-point boundary value problems in the reproducing kernel space

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