In this study, based on the optimal free derivative without memory methods proposed by Cordero et al. [A. Cordero, J.L. Hueso, E. Martinez, J.R. Torregrosa, Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation, Mathematical and Computer Modeling. 57 (2013) 1950-1956], we develop two new iterative with memory methods for solving a nonline...

This work addresses the problem of computing the time evolution of the probability density function (pdf) of the state in a nonlinear neuromuscular blockade (NMB) model, assuming that the source of uncertainty is the knowledge about one parameter. The NMB state is enlarged with the parameter, that verifies an equation given by its derivative being zero and has an initial condition described by ...

In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian...

in this paper, we use a combination of legendre and block-pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.the nonlinear part of the integral equation is approximated by hybrid legen-dre block-pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. we give some numerical examples. to showapplicability of...

In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based ...

We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L(H ; ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under bo...

In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled Adomian decomposition method has been defined applied to solve newly dispersion. The approximate analytical solutions are obtained compared each other graphically.

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigat...