RESEARCH ARTICLE
A space–time spectral Petrov–Galerkin method for nonlinear time fractional Korteweg–de Vries–Burgers equations
Zhe Yu,
Jiebao Sun,
Boying Wu,
Zhe Yu
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Search for more papers by this authorCorresponding Author
Jiebao Sun
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Correspondence
Jiebao Sun, Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, China.
Email: [email protected]
Communicated by: J. Banasiak
Search for more papers by this authorBoying Wu
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Search for more papers by this authorZhe Yu,
Jiebao Sun,
Boying Wu,
Zhe Yu
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Search for more papers by this authorCorresponding Author
Jiebao Sun
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Correspondence
Jiebao Sun, Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, China.
Email: [email protected]
Communicated by: J. Banasiak
Search for more papers by this authorBoying Wu
Department of Mathematics, Harbin Institute of Technology, Harbin, China
Search for more papers by this authorAbstract
In this work, we study a space–time Petrov–Galerkin method for third- and fifth-order time fractional Korteweg–de Vries–Burgers equations. The method is based on the framework of Legendre and Jacobi polynomials. The basis functions of the fractional part are constructed by the generalized Jacobi functions, which contained the singularity of weak solutions. The numerical schemes of the problems are transformed into the nonlinear schemes constructed by matrices. Based on the orthogonality of ideal basis functions, we get the optimal estimation under the specific weighted Sobolev spaces. Numerical experiments confirm the expected convergence.
CONFLICT OF INTEREST
This work does not have any conflicts of interest.
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