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Full-Text Articles in Physical Sciences and Mathematics
Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova
Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova
Mathematics Faculty Publications
The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.
The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao
The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao
Mathematics Faculty Publications
The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.
Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe
Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe
Mathematics Faculty Publications
The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.