The heat transfer for a non-Newtonian power-law fluid over a moving surface is investigated by applying a uniform suction/injection velocity profile. The flow is influenced by internal heat generation/absorption. The energy equation is solved at constant surface temperature condition. The Merk-Chao series is applied to obtain a set of ODEs instead of a complicated PDE. The converted ordinary diffe...

One of the central problems of mathematics in the second half of the 19th century and at the beginning of the 20th century was the problem of uniformization of Riemann surfaces. The classics, Klein [1] and Poincaré [2], associated it with studying second-order ordinary differential equations with regular singular points. Poincaré proposed another approach to the uniformization problem [3]. It c...

If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...

We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete φ lattice and the discrete sine–Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

This paper extends the application of the differential quadrature method (DQM) to high order (2 3rd) ordinary differential equations with the boundary conditions specified at multiple points (2 three different points). Explicit weighting coefficients for higher order derivatives have been derived using interpolating trigonometric polynomials. A three-point, linear third-order differential equat...

In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy minimization leads to representation as a nonlinear fourth-order ordinary differential equation, for which we prove there exists a unique solution. Drawing parallels...