Quasilinearization and rate of convergence for higher-order nonlinear periodic boundary-value problems

DOI10.1023/A:1026413921997zbMath0976.34015WikidataQ60199464 ScholiaQ60199464MaRDI QIDQ5929427

Juan. J. Nieto, Alberto Cabada

Publication date: 12 December 2001

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

upper and lower solutionsboundary value problemsquasilinearizationrapid convergence

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Ordinary differential equations with impulses (34A37) Theoretical approximation of solutions to ordinary differential equations (34A45)

Related Items (23)

Improved generalized quasilinearization method and rapid convergence for reaction diffusion equations ⋮ Existence and quasilinearization in Banach spaces ⋮ A quasilinearization method for a class of integro-differential equations with mixed nonlinearities ⋮ Rapid convergence of solution for hybrid system with causal operators ⋮ Approximation of solutions for second-order \(m\)-point nonlocal boundary value problems via the method of generalized quasilinearization ⋮ Two-grid quasilinearization approach to ODEs with applications to model problems in physics and mechanics ⋮ Existence and approximation of solution of three-point boundary value problems on time scales ⋮ Solvability and dependence on a parameter of a fourth-order periodic boundary value problem ⋮ Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions ⋮ Method of quasilinearization for a nonlocal singular boundary value problem in weighted spaces ⋮ The generalized quasilinearization method and three point boundary value problems on time scales ⋮ A generalized quasilinearization method for nonlinear second-order impulsive differential equations involving the \(p\)-Laplacian ⋮ Generalized quasilinearization method and higher order of convergence for second-order boundary value problems ⋮ Odd periodic solutions for 2\(n\)th-order ordinary differential equations ⋮ Approximation of solutions for an initial and terminal value problem for the forced Duffing equation with non-viscous damping ⋮ Approximation of solutions of the nonlinear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions ⋮ Existence and approximation of solutions of forced Duffing type integro-differential equations with three-point nonlinear boundary conditions ⋮ Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions ⋮ Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions ⋮ On the existence and uniqueness for higher order periodic boundary value problems ⋮ Existence and analytic approximation of solutions of Duffing type nonlinear integro-differential equation with integral boundary conditions ⋮ A quasilinearization approach for two point nonlinear boundary value problems on time scales ⋮ Nontrivial solutions of a fully fourth-order periodic boundary value problem

Cites Work

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• On the use of the quasilinearization method in the growth of a pathogenic bacteria
• Rapid convergence of the iterative technique for first order initial value problems
• Extension of the method of quasilinearization and rapid convergence
• Parallel computation of two-point boundary-value problems via particular solutions
• The method of lower and upper solutions for \(n\)th-order periodic boundary value problems
• The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems
• The method of lower and upper solutions for third-order periodic boundary value problems
• Maximum principles for fourth and sixth order periodic boundary value problems

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