In this paper, a Chebyshev spectral collocation domain decomposition (DD) semidiscretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s–Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation...

We present a finite element scheme capable of preserving the nonnegative and bounded solutions of the generalized Burgers-Huxley equation. Proofs of existence and uniqueness of a solution to the continuous problem together with some results concerning the boundedness and the nonnegativity of the solution are given. Under appropriate conditions on the mesh and the initial and boundary data, boun...

A generalized dimensional analysis performed by using Buckingham’s Pi-theorem for the generalized Burgers’ equation is presented. The application of the Buckingham Pi-theorem is used to reduce the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with appropriate corresponding conditions. By using a scaling invariant we simplif...

Numerical solutions of the generalized Burgers-Huxley equation are obtained using a polynomial differential quadrature method with minimal computational effort. To achieve this, a combination of a polynomial-based differential quadrature method in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time has been used. The computed results with the use of this t...

The contraction of a muscle generates a force that decreases when increasing the contraction velocity. This "hyperbolic" force-velocity relationship has been known since the seminal work of A. V. Hill in 1938 [Hill AV (1938) Proc R Soc Lond B Biol Sci 126(843):136-195]. Hill's heuristic equation is still used, and the sliding-filament theory for the sarcomere [Huxley H, Hanson J (1954) Nature 1...