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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems, Paul W. Eloe, Johnny Henderson, Rahmat Ali Khan
Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems, Paul W. Eloe, Johnny Henderson, Rahmat Ali Khan
Mathematics Faculty Publications
No abstract provided.
A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman
A Study Of The Gam Approach To Solve Laminar Boundary Layer Equations In The Presence Of A Wedge, Rahmat Ali Khan, Muhammad Usman
Mathematics Faculty Publications
We apply an easy and simple technique, the generalized ap- proximation method (GAM) to investigate the temperature field associated with the Falkner-Skan boundary-layer problem. The nonlinear partial differ- ential equations are transformed to nonlinear ordinary differential equations using the similarity transformations. An iterative scheme for the non-linear ordinary differential equations associated with the velocity and temperature profiles are developed via GAM. Numerical results for the dimensionless ve- locity and temperature profiles of the wedge flow are presented graphically for different values of the wedge angle and Prandtl number.
A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman
A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman
Mathematics Faculty Publications
In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.
Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul
Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul
Mathematics Faculty Publications
Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.
A Leggett-Williams Type Theorem Applied To A Fourth Order Problem, Richard Avery, Paul Eloe, Johnny Henderson
A Leggett-Williams Type Theorem Applied To A Fourth Order Problem, Richard Avery, Paul Eloe, Johnny Henderson
Mathematics Faculty Publications
We apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a fourth order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach spstce. Inequalities that extend the notion of concavity to fourth order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
The Role Of Concavity In Applications Of Avery Type Fixed Point Theorems To Higher Order Differential Equations, Abdulmalik A. Altwaty, Paul W. Eloe
The Role Of Concavity In Applications Of Avery Type Fixed Point Theorems To Higher Order Differential Equations, Abdulmalik A. Altwaty, Paul W. Eloe
Mathematics Faculty Publications
In this article we apply an extension of an Avery type fixed point theorem to a family of boundary value problems for higher order ordinary differential equations. The theorem employs concave and convex functionals defined on a cone in a Banach space. We begin by extending a known application to a right focal boundary value problem for a second order problem to a conjugate boundary value problem for a second order problem. We then extend inductively to a two point boundary value problem for a higher order equation. Concavity of differentiable functions plays a key role in the application to …