One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...

We consider second-order linear differential equations φ(x)y′′ + f(x)y′ + g(x)y = h(x) in the interval (−1, 1) with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions. We consider φ(x), f(x), g(x) and h(x) analytic in a Cassini disk with foci at x = ±1 containing the interval (−1, 1). The two-point Taylor expansion of the solution y(x) at the extreme points ±1 is used to give a c...

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

In this article, we prove the existence of solutions to mixed twopoint boundary-value problem for impulsive differential equations by variational methods, in both resonant and the non resonant cases.

We study the discrete approximation to solutions of first-order system arising from applying the trapezoidal rule to a second-order scalar ordinary differential equation. In the trapezoidal rule the finite difference approximation are Dyk = (zk + zk−1)/2, Dzk = ( fk + fk−1)/2, for k = 1, 2, .., n, and tk = kh for k = 0, ..., n, 0 = G ( (y0, yn), (z0 + z1)/2, (zn−1 + zn)/2) ) , where fi ≡ f (ti,...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary differential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate. Received: 2 February 2014, Revised: 4 May 201...