In this paper, we investigate the new traveling wave solutions for sixth-order Boussinesq equation using tanh-coth method. Such a method is type of expansion that represents partial differential equations as polynomials $\tanh$ and $\coth$ functions. We discover several with different parameters, which are fundamental importance various applications.

In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results  how that the simplicity and efficiency of this method.

we present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. numerical method of sixth-order with end conditions of the order 6 is derived. the convergence analysis of the method has been discussed. numerical examples are presented to illustra...

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

This is the first of three papers on the geometric and combinatorial characterization of global Sturm attractors which consist of a single closed 3-ball. The underlying scalar PDE is parabolic, ut = uxx + f(x, u, ux) , on the unit interval 0 < x < 1 with Neumann boundary conditions. Equilibria are assumed to be hyperbolic. The geometric description is in terms of the regular cell complex define...

We have formalised the Sturm-Tarski theorem (also referred as the Tarski theorem): Given polynomials p, q ∈ R[x], the Sturm-Tarski theorem computes the sum of the signs of q over the roots of p by calculating some remainder sequences. Note, the better-known Sturm theorem is an instance of the Sturm-Tarski theorem when q = 1. The proof follows the classic book by Basu et al. [1] and Cyril Cohen’...