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...

We obtain oscillation criteria for a second order self-adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function. We illustrate our results with some nontrivial examples.

In this work we deal with a Backward doubly stochastic differential equation (BDSDE) associated to a random Poisson measure. We establish existence and uniqueness of the solution in the case of non-Lipschitz coefficients.

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Mathias Masson Name of the doctoral dissertation Regularity for parabolic quasiminimizers in metric measure spaces Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 89/2013 Field of research Mathematical analysis Manuscript submitte...

We consider a dynamical system described by the differential equation ˙ Y t = −U ′ (Y t) with a unique stable point at the origin. We perturb the system by Lévy noise of intensity ε, to obtain the stochastic differential equation dX ε t = −U ′ (X ε t−)dt + εdL t. The process L is a symmetric Lévy process whose jump measure ν has exponentially light tails, ν([u, ∞)) ∼ exp(−u α), α > 0, u → ∞. We...