We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the solution space, the original problem is reformulated as a partial differential algebraic equation system by decomposing the solution into a group component and a sp...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

Here, Adomian decomposition method has been used for finding approximateand numerical solutions of nonlinear differential difference equations arising inmathematical physics. Two models of special interest in physics, namely, theHybrid nonlinear differential difference equation and Relativistic Toda couplednonlinear differential-difference equation are chosen to illustrate the validity andthe g...

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large eld called ne...

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...

The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation r t x′ t γ ′′ p t x τ t 0, where studied equation is in a canonical form, that is, ∫∞ r −1/γ s ds ∞. Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained esse...