The El Nino–Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean–atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.

http://iopscience.iop.org/article/10.1088/1674-1056/17/2/002/pdf

Asymptotic solution for a class of sea—air oscillator model for El Niño—southern oscillation

A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.

Asymptotic Solution of Activator Inhibitor Systems for Nonlinear Reaction Diffusion Equations

A class of perturbed mechanisms for the western boundary undercurrents in the Pacific is considered. The model of generalized governing equations is studied. Employing the method of variational iteration, an approximate solution of corresponding model is obtained. It is proved from the results that the solution for the variational iteration method can be used for analysing operation of the perturbed mechanism of western boundary undercurrents in the Pacific.

Variational iteration method for solving perturbed mechanism of western boundary undercurrents in the Pacific

A new way to solve singular perturbation problems is introduced. It is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). In this paper, we consider singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. An initial-value technique is used for its solution. However, this technique is based on the boundary layer behavior of the solution. It is distinguished by the following fact: The original second order problem is replaced by an asymptotically equivalent first-order problem and is solved as an initial-value problem via cubic spline. Numerical experience with several linear and non-linear examples is described. It is observed that the present method approximates the exact solution very well.

An Initial-Value Technique for Singularly Perturbed Boundary Value Problems via Cubic Spline

The EI Nino and Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific sea–air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea–air oscillator for the ENSO model.

The homotopic method of travelling wave solution for El Niño tropic sea–air coupled oscillator

A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.

Jia-qi Mo

Papers

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation