Forced perturbed Korteweg-de Vries equation in an elastic tube filled with a viscous fluid

Numerical Solutions of the Forced Perturbed Korteweg-De Vries Equation With Variable Coefficients

“…It has been used to solve the KdV [13], Burgers [14] and KdV-Burgers equations [15]. The Chan and Kerkhoven [13] scheme is extended for the FpKdV equation (1). The FpKdV equation (1) is integrated in space τ by the leapfrog finitedifference scheme in the spectral time ξ.…”

“…Tay [1] studied small-but-finite amplitude weakly nonlinear wave propagation in a prestressed fluid-filled elastic tube with a symmetrical setenosis filled with a Newtonian fluid by applying the reductive perturbation method in the long wave approximation. By using the stretched coordinate of boundary-value type and extending the field quantities into the asymptotic series of order ǫ, where ǫ is a small parameter, the governing equations are reduced to the Forced perturbed Korteweg-de Vries (FpKdV) equation with variable coefficients…”

“…The presence of forcing term, µ(τ ) and variable coefficient term, µ 4 (τ )U ξ are due to the presence of stenosis, while the perturbed term µ 5 U is caused by Newtonian fluid. The coefficients of µ 1 , µ 3 , µ 4 (τ ), µ 5 and µ(τ ) are defined by [1] as…”

“…Since then, the KdV equation has been found to describe many physical phenomena, including long internal waves in ocean, magneto hydrodynamics waves in warm plasma, ion acoustic waves in a plasma, acoustic waves on a crystal lattice and wave propagation in an elastic tube filled with an inviscid fluid. Many studies have been devoted to the numerical solutions of the KdV equation (5), however, none of the literature works dealt with numerical solutions of the FpKdV equation (1). Motivated with the works of wave propagation which yielded the FpKdV equation (1) as well as numerical methods, we are going to find numerical solution of the FpKdV by two numerical methods, namely method of line (MOL) and pseudospectral.…”

“…Motivated with the works of wave propagation which yielded the FpKdV equation (1) as well as numerical methods, we are going to find numerical solution of the FpKdV by two numerical methods, namely method of line (MOL) and pseudospectral. The numerical solution of the FpKdV equation is then compared in terms of its maximum absolute error at certain space with progressive wave solution conducted by [1].…”