To integrate large systems of ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on embedded, explicit Runge-Kutta (RK) formulas. The order of accuracy of such methods depends on interpolating certain solution components with a polynomial of sufficiently high degree. By analyzing the method applied to a simple test eq...

A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...

and Applied Analysis 3 Motivated by 14, 15 , here we study the existence of AL-solutions for 1.1 . The approach is completely different from the one used in 15 , in which an iteration process, jointly with a comparison with the linear equation y 4 q t y 2 0, is employed. Our tools are based on a topological method, certain integral inequalities, and some auxiliary functions. In particular, for ...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...

We study the existence and multiplicity of nontrivial periodic solutions for a semilinear fourth-order ordinary differential equation arising in the study of spatial patterns for bistable systems. Variational tools such as the Brezis–Nirenberg theorem and Clark theorem are used in the proofs of the main results. © 2004 Elsevier Ltd. All rights reserved. MSC: 34B15; 34C25; 35K35

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

This paper studies nonlinear wave propagation in a bubble-liquid mixture based on the third-order Kudryashov–Sinelshchikov (KS) equation. Symmetry is classified and reduced through symmetry group method. Through generalized conditional method, this equation classified, considered are second, third, fourth, fifth-order, respectively. Meanwhile, equations transformed into system of ordinary diffe...

In this work, the authors consider the fourth order nonlinear ordinary differential equation u(4)(t) = f (t, u(t)), 0 < t < 1, with the four-point boundary conditions u(0) = u(1) = 0, au′′(ξ1)− bu′′′(ξ1) = 0, cu′′(ξ2)+ du′′′(ξ2) = 0, where 0 ≤ ξ1 < ξ2 ≤ 1. By means of the upper and lower solution method and fixed point theorems, some results on the existence of positive solutions to the above f...