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Duffing equation can describe many important nonlinear physical systems. In this paper a coupled approach based on quasilinearization and Bessel polynomial collocation method has been suggested to solve nonlinear duffing oscillator equation. The nonlinearity in duffing oscillator can be of various variety. This approach is very efficient, stable and reliable to deal with any kind of nonlinearity. Numerical examples demonstrate the validity and applicability of the approach on various types of nonlinear duffing oscillator equation.

This paper presents a coupled approach to solve the Kuramoto-Shivashinsky equations. This approach isa combination of modified variation iteration method and a rational approximation by mathematical software MATHEMATICA. Numerical examples illustrate that this combination of two techniques improves accuracy.

In this paper, Improved Iteration Method (IIM) is proposed for the thermal analysis of some fin problems. Fin is the extended surface that helps to transfer heat from hot body to the external environment. Thermal efficiency of fin can be analyzed with the help of temperature distribution of fin, which can be modelled by nonlinear differential equation. The efficiency and accuracy of the proposed method is demonstrated by solving few nonlinear fin problems with different values of thermal conductivity parameter. The numerical results obtained by the proposed method show the excellent agreement with exact solution as well as with the solutions obtained by some recently developed methods. Convergence analysis of the proposed method has also been discussed.

In this paper, a modified iteration method (MIM) has been proposed to solve nonlinear second-order ODEs. Convergence analysis and error estimate of the proposed method are also discussed. Computational efficiency of this method is illustrated through numerical examples.

Lane–Emden type equations have been interesting since long time due to their wide applications in mathematical physics and astrophysics. In this paper, a coupled approach has been proposed for the solution of nonlinear singular value problems of Lane–Emden type.

In this paper, a coupled approach based on an integral operator and polynomial least square method is introduced to solve a singular initial value problem: Lane–Emden equation. In this approach first, using an integral operator, Lane–Emden equation is converted into nonlinear Volterra integral equation which is further solved using polynomial least square method. The accuracy and validity of the method are demonstrated using many numerical examples.

Many physical phenomena can be modeled by partial differential equations with singularities and interfaces. The standard finite difference and finite element methods may not be successful in giving satisfactory numerical results for such problems. Hence, many new methods have been developed. Some of them are developed with the modifications in the standard methods, so that they can deal with the discontinuities and the singularities. In this article, a survey has been done on some recent efficient techniques to solve elliptic interface problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 94-114, 2012

The study of heat conduction in multilayered composite bodies is of great interest because of their importance in many engineering applications. Steady state heat conduction in bodies made of different material layers which have different thermal conductivities is governed by elliptic boundary value problem with interfaces. Solution of the corresponding problem is often difficult because of the discontinuity across the interface. In this paper, a mathematical model of such problems has been described and computer simulation of two such problems has been presented using decomposed immersed interface method using MATLAB.