Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems

Chang, Shih-Hsiang

doi:10.1007/s12190-020-01496-4

Cited by 3 publications

(2 citation statements)

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“…The existence and uniqueness results for the solution of the problems Eq. (3)-( 4) are given in [13], [6] and [3]. The Green's function G(t, s) corresponding to linear term in Eq.…”

Section: Greens Function and Methodologymentioning

confidence: 99%

“…For instance, in mathematical modeling applications of a two-dimensional channel with porous walls, deformation of elastic beams, fluid dynamics. These problems have been studied by several mathematicians(see [11], [1], [4], [7], [2], [3], [8], [5], [15], [14] and the references therein. [11] converted the BVP to Initial Value Problem (IVP) and solved the linear equation while [13] solved the problem by transforming the fourth-order BVP to third-order BVP and applied by contracting mapping principle.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

Akgün

Rasulov

2021

Eur. J. Pure Appl. Math.

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“…The existence and uniqueness results for the solution of the problems Eq. (3)-( 4) are given in [13], [6] and [3]. The Green's function G(t, s) corresponding to linear term in Eq.…”

Section: Greens Function and Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

Akgün

Rasulov

2021

Eur. J. Pure Appl. Math.

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An Efficient Iterative Method for Nonlinear Boundary Value Problems with Existence and Uniqueness

Chang

2022

Int. J. Comput. Methods

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A simple and efficient iterative method involving Green’s function is presented for solving the general [Formula: see text]th-order nonlinear boundary value problems. Existence and uniqueness results for such problems are established using the fixed-point theorems. This guarantees the uniform convergence of the proposed iterative algorithm. The resulting iterative solutions does not contain any unknown constants and automatically satisfy the given boundary conditions. This gives the iterative method much wider applicability in obtaining the analytical or numerical solution of the problem. The performance of the proposed approach is assessed and tested on four examples.

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The reproducing kernel method for nonlinear fourth-order BVPs

Wang,

Lv,

2023

MATH

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<abstract><p>Based on the reproducing kernel theory, we solve the nonlinear fourth order boundary value problem in the reproducing kernel space $ W_{2}^{5}[0, 1] $. Its approximate solution is obtained by truncating the n-term of the exact solution and using the $ \varepsilon $-best approximate method. Meanwhile, the approximate solution $ u^{(i)}_{n}(x) $ converges uniformly to the exact solution $ u^{(i)}(x), (i, 0, 1, 2, 3, 4) $. The validity and accuracy of this method are verified by some examples.</p></abstract>

show abstract

Existence-uniqueness and fixed-point iterative method for general nonlinear fourth-order boundary value problems

Cited by 3 publications

References 18 publications

Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

Generalized Iteration Method via Green's Function for the Solution of the Fourth-order Boundary Value Problems

An Efficient Iterative Method for Nonlinear Boundary Value Problems with Existence and Uniqueness

The reproducing kernel method for nonlinear fourth-order BVPs

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