Theoretical and Numerical Aspects of a Third-order Three-point Nonhomogeneous Boundary Value Problem

MARTINEZ, A. L. M.; FERREIRA, M. R. A.; CASTELANI, E. V.

doi:10.5540/tema.2019.020.03.0417

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Articles • TEMA (São Carlos) 20 (3) • Sep-Dec 2019 • https://doi.org/10.5540/tema.2019.020.03.0417 copy

Theoretical and Numerical Aspects of a Third-order Three-point Nonhomogeneous Boundary Value Problem

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

In this paper we are considering a third-order three-point equation with nonhomogeneous conditions in the boundary. Using Krasnoselskii’s Theorem and Leray-Schauder Alternative we provide existence results of positive solutions for this problem. Nontrivials examples are given and a numerical method is introduced.

Key words
numerical solutions; third-order; boundary value problem; Krasnoselskii’s Theorem

It	$ε_{u}^{k}$	$ε^{k}$	${\bar{ε}}^{k}$
1	0.104585227251908	0.355112466879952	1.000000000000000
2	0.072538564385106	0.032046662866802	0.082773878760819
3	0.069264937033799	0.003273627351307	0.008384612437847
4	0.068925441261629	0.000339495772170	0.000868781674432
5	0.068890166416009	0.000035274845620	0.000090261428243

It	$ε_{u}^{k}$	$ε^{k}$	${\bar{ε}}^{k}$
1	-	0.168278823890335	1.000000000000000
2	-	0.007563461402919	0.043012756518181
3	-	0.000744660869474	0.004216964422657
4	-	0.000077049209989	0.000436134198292

It	$ε_{u}^{k}$	$ε^{k}$	${\bar{ε}}^{k}$
1	-	0.740971458506793	1.000000000000000
2	-	0.010141509530254	0.013876702158219
3	-	0.000276799190473	0.000378602975785
4	-	0.000007307338952	0.000009995000056

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[1] *Corresponding author: André L. M. Martinez – E-mail: andrelmmartinez@yahoo.com.br – https://orcid.org/0000-0003-1888-648X