generalized solution on neumann problem of the fourth order ordinary dierential equation in space w2 (0; b) has been discussed , we obtain the condition on b.v.p when the solution is in classical form. formulation of quintic spline function has been derived and the consistency relations are given.numerical method,based on quintic spline approximation has been developed. spline solution of the...

So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...

We consider a system of ordinary di erential equations consisting of a singularly perturbed scalar di erential equation of second order and a scalar di erential equation of rst or second order and study a Neuman-Cauchy or a Neuman-Dirichlet problem. We assume that the degenerate equation has two intersecting solutions such that the standard theory for systems of Tichonov's type cannot be applie...

We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

In this paper, we study general linear systems of delay di erential-algebraic equations (DDAEs) of arbitrary order. We show that under some consistency conditions, every linear high-order DAE can be reformulated as an underlying high-order ordinary di erential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay di erential equation (DDE). We der...

in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

One of the most important theorems in Ordinary Di↵erential Equations is Picard’s Existence and Uniqueness Theorem for first-order ordinary di↵erential equations. Why is Picard’s Theorem so important? One reason is it can be generalized to establish existence and uniqueness results for higher-order ordinary di↵erential equations and for systems of di↵erential equations. Another is that it is a g...

In this thesis we study numerical methods for simulating mechanical deformations of cell membranes. Such models are given in terms of fourth order partial di erential equations. In order to enable comparisons of the models predictions to experimental results, the equations must be solved on arbitrary cell geometries. A Finite Element Method based on subdivision surfaces, which is capable of dis...