2019 **Abstract:** This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation are first approximated by interpolating polynomials and then discretized at the Chebyshev–Gauss–Lobatto points. Thus, we get a system of algebraic equations whose solution is the set of unknown coefficients of the approximate solution of the main problem. We investig…

Help me understand this report

Search citation statements

Paper Sections

Select...

2

Citation Types

0

2

0

Year Published

2022

2022

Publication Types

Select...

2

Relationship

0

2

Authors

Journals

(2 citation statements)

(67 reference statements)

0

2

0

“…This is why in practical calculations often small artificial damping is added to the model. (3) Spatial-temporal semianalytical basis function methods [37][38][39] employ the spatial-temporal semi-analytical basis function a priori to satisfy the transient wave equation and then solve it directly. Among these three time-discretization schemes, the first two have been widely used for transient wave propagation analysis; the last one has not been widely used because the time-dependent semi-analytical basis functions are not easy to construct, in particular, the transient wave equation, including the source excitations.…”

confidence: 99%

“…This is why in practical calculations often small artificial damping is added to the model. (3) Spatial-temporal semianalytical basis function methods [37][38][39] employ the spatial-temporal semi-analytical basis function a priori to satisfy the transient wave equation and then solve it directly. Among these three time-discretization schemes, the first two have been widely used for transient wave propagation analysis; the last one has not been widely used because the time-dependent semi-analytical basis functions are not easy to construct, in particular, the transient wave equation, including the source excitations.…”

confidence: 99%

“…We fully show that the approximate solutions are convergent to the exact solution when the number of collocation points tends to infinity. Note that spectral collocation methods have high accuracy and exponential convergence and, up to now many researchers utilized them to solve different continuous-time problems involving the ordinary and partial differential equations [12,13,18].…”

confidence: 99%