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, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

‎‎‎‎‎‎‎‎‎‎‎‎‎This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product‎. ‎The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra integro--differential equations‎ which appear in various fields of science such as physics and engineering. ‎The Operational matr...

The present author recently proposed and proved a relationship theorem between nonlinear polynomial equations and the corresponding Jacobian matrix. By using this theorem, this paper derives a Newton iterative formula without requiring the evaluation of nonlinear function values in the solution of nonlinear polynomial-only problems.

A wavelet collocation method for nonlinear Hammerstein equations is formulated. A sparsity in the Jacobian matrix is obtained which gives rise to a fast algorithm for nonlinear solvers such as the Newton’s method and the quasi-Newton method. A fast multilevel augmentation method is developed on a transformed nonlinear equation which gives an additional saving in computational time.

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.

the nonlocal nonlinear buckling of a double layer graphene sheet (dlgs) covered by zinc oxide (zno) piezoelectric layers is investigated in this study. the surrounding circumstances of the system are considered as a pasternak foundation including spring constants and a shear layer. graphene sheets are subjected to longitudinal magnetic field and biaxial forces. on the other hand, the zno piezoe...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

We study matrix generalizations of derivative nonlinear Schrödinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are ‘C-integrable’ and the rest of them are ‘S-integrable’ in Calogero’s terminology. PACS numbers: 02.10Jf, 02.30.Jr, 03.65.Ge, 11.30.-j Submitted to: Inverse Problems † E-mail address: [email protected]...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...