Numerical solutions of linear and nonlinear singular perturbation problems

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Solutions of Nonlinear Integral Equations and Their Application to Singular Perturbation Problems Thesis By

Sufficient conditions for the existence and uniqueness, and estimates, of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived. A successive approximation technique involving a double sequence is used in the proof . This integral equation result is applied to the second order singular perturbation proble...

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type

numerical solutions of two-dimensional linear and nonlinear volterra integral equations: homotopy perturbation method and differential transform method