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...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

in this paper, the dierential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. these resultsshow that this technique is easy to apply.

We studied the Cauchy problem of fuzzy di erential equations on the basis of introducing the concept of di erentiation which is a generalization of the de nition of H-di erentiability due to Puri and Ralescu (1983), for fuzzy set-valued mappings of real variables whose values are in the fuzzy number space (E; D). The existence and uniqueness theorem is obtained for the Cauchy problem x′=f(t; x)...

In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

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 paper, a new and ecient approach based on operational matrices with respect to the gener-alized laguerre polynomials for numerical approximation of the linear ordinary dierential equations(odes) with variable coecients is introduced. explicit formulae which express the generalized la-guerre expansion coecients for the moments of the derivatives of any dierentiable function in terms...

First order neutral di¤erential equations are studied and su‰cient conditions are derived for every solution to be oscillatory. Our approach is to reduce the oscillation of neutral di¤erential equations to the nonexistence of eventually positive solutions of non-neutral di¤erential inequalities. Our results extend and improve several known results in the literature.