Shock waves and compactons for fifth-order non-linear dispersion equations

Shock Waves and Compactons for Fifth-order Nonlinear Dispersion Equations

The following question is posed: to justify that the standing shock wave S−(x) = −signx = − { −1 for x < 0, 1 for x > 0, is a correct “entropy” solution of fifth-order nonlinear dispersion equations (NDEs), ut = −(uux)xxxx and ut = −(uuxxxx)x in R × R+. These two quasilinear degenerate PDEs are chosen as typical representatives, so other similar (2m+ 1)th-order NDEs with no divergence structure...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order

In this paper, we establish sufficient conditions under which all solutions of equation of the type x(5) + f(t, x, ẋ, ẍ, ... x , x(4)) + φ(t, ẋ, ẍ, ... x ) + ψ(t, x, ẋ, ẍ) + g(t, x, ẋ) + e(t)h(x) = p(t, x, ẋ, ẍ, ... x , x(4)) are uniformly bounded and tend to zero as t → ∞. Our theorem is stated in a more general form; it extends some related results known in the literature. Also, the relevance...

NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Modified homotopy perturbation method for solving non-linear oscillator's ‎equations

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...