in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prim...

in this work the collocation method based on quartic b-spline is developed and applied to two-point boundary value problem in ordinary diferential 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.

in this paper a mathematical simulation of a simplified internal combustion engine is presented. to contribute engine kinematics and its geometry, simple relations are derived for constrained motions. the equation of motion for the piston forms a singular boundary value problem. the uniqueness of the solution was studied in the banach space. for solving governing equations an iterative numerica...

in this paper, we investigate the total variation diminishing property for a class of 2-stage explicit rung-kutta methods of order two (rk2) when applied to the numerical solution of special nonlinear initial value problems (ivps) for (odes). schemes preserving the essential physical property of diminishing total variation are of great importance in practice. such schemes are free of spurious o...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.