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A new stable collocation method for solving a class of nonlinear fractional delay differential equations
- Source :
- Numerical Algorithms. 85:1123-1153
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- In this paper, a stable collocation method for solving the nonlinear fractional delay differential equations is proposed by constructing a new set of multiscale orthonormal bases of$W^{1}_{2,0}$W2,01. Error estimations of approximate solutions are given and the highest convergence order can reach four in the sense of the norm of$W_{2,0}^{1}$W2,01. To overcome the nonlinear condition, we make use of Newton’s method to transform the nonlinear equation into a sequence of linear equations. For the linear equations, a rigorous theory is given for obtaining theirε-approximate solutions by solving a system of equations or searching the minimum value. Stability analysis is also obtained. Some examples are discussed to illustrate the efficiency of the proposed method.
- Subjects :
- Applied Mathematics
Numerical analysis
Order (ring theory)
010103 numerical & computational mathematics
Delay differential equation
System of linear equations
01 natural sciences
010101 applied mathematics
Nonlinear system
Collocation method
Applied mathematics
Orthonormal basis
0101 mathematics
Linear equation
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 85
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........8572e183c67063f47814ac7255d1ddc1