Some oscillation criteria for solutions of a general ordinary differential equation of second order of the form (r(t)ψ(x(t))ẋ(t))+h(t)ẋ(t)+q(t)φ(g(x(t)),r(t)ψ(x(t))ẋ(t)) = H(t,x(t), ẋ(t)) with alternating coefficients are discussed. Our results improve and extend some existing results in the literature. Some illustrative examples are given with its numerical solutions which are computed using R...

In the present paper, we discuss three point difference method based on nonpolynomial spline basis for the second order ordinary differential equation. Difference schemes are derived for linear and nonlinear case and are used to solve via two parameter alternating group explicit iterative algorithm. The schemes have a fourth and second order of uniform convergence for the choice of the paramete...

In this paper we discuss the numerical solution of initial-boundary value problem for the fourth order parabolic partial integro-differential equation. We use the forward Euler scheme for time discretization and the quasi-wavelet method for space discretization. Sometimes, we give a new method about the treatment of boundary condition. Numerical experiment is included to demonstrate the validit...

The DI methods for directly solving a system ofa general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergencefor the variable order and stepsize case.

tension-leg platform (tlp) is a vertically moored floating structure. the platform is permanently mooredby tendons. surge equation of motion of tlp is highly nonlinear because of large displacement and it should be solved with perturbation parameter in time domain. this paper compare the dynamic motion responses of a tlp in regular sea waves obtained by applying three method in time domain usin...

The variational iteration method [1, 2], which is a modified general Lagrange multiplier method, has been shown to solve effectively, easily, and accurately a large class of nonlinear problems with approximations which converges (locally) to accurate solutions (if certain Lipschitz-continuity conditions are met). It was successfully applied to autonomous ordinary differential equations and nonl...

Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured-segregated model is used f...