In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...

In this study, we propose four methods for the analytical solution of second order ordinary non-homogeneous differential equations with variable coefficients. first case, method directly gives in explicit or integral form. method, problem reduces to solutions adjoined equation homogeneous type. As long as two can be solved, always found. third is transformed into Riccati equation. solved by mea...

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing three translation equation, fourth-order ordinary differential is obtained solved in terms an incomplete elliptic integral. Moreover, with aid Kudryashov’s approach, more closed-form solutions cons...

Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science engineering. In present work, we suggest a procedure, extending our previous research results, to represent solutions nonlinear differential problems fourth order given form Y(4)(x)=f(x,Y(x)) terms higher-order splines. The corresponding algorithm is expl...

We investigate the breathing of optical spatial solitons in highly nonlocal media. We use a generalization of the Ehrenfest theorem (1990 Am. J. Phys. 58 742) leading to a fourth-order ordinary differential equation, the latter ruling the beam width evolution in propagation. In actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell (1997 Science 276 1538)...