Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) is a nonlinear state-feedback control approach which can be used for stabilization and tracking control of a wide range of physical systems. Among many variants of this technique, algebraic IDA-PBC is by far the simplest method as it involves differential-algebraic equations rather than partial-differential equations. Howe...

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...

When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the...

Lane-Emden equation is a nonlinear singular equation that plays an important role in the astrophysics. In this paper, we have applied the collocation method based on rational Chebyshev functions to solve Lane-Emden type equations. The method reduces solving the nonlinear ordinary differential equation to solving a system of nonlinear algebraic equations. The comparison of the results with the o...

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

Second-kind Volterra integral equations with weakly singular kernels typically have solutions which are nonsmooth near the initial point of the interval of integration. Using an adaptation of the analysis originally developed for nonlinear weakly singular Fredholm integral equations, we present a complete discussion of the optimal (global and local) order of convergence of piecewise polynomial ...

WAVEFORM RELAXATION METHODS OF NONLINEAR INTEGRAL-DIFFERENTIAL-ALGEBRAIC EQUATIONS ∗1) Yao-lin Jiang (Department of Mathematical Sciences, Xi’an Jiaotong University, Xi’an 710049, China) Abstract In this paper we consider continuous-time and discrete-time waveform relaxation methods for general nonlinear integral-differential-algebraic equations. For the continuous-time case we derive the conve...

In this work, an efficient numerical method for the complex solutions of nonlinear partial differential equations based on the direct algebraic approach is proposed, and tested in the case of generalized Burgers–Huxley equation ∂u ∂t + αu ∂u ∂x − ∂ u ∂x2 = βu(1− u)(u − γ) Whenα = 0, δ = 1, is reduced to the Huxley equation. The proposed scheme can be used in a wide class of nonlinear reaction–d...