A new stable collocation method for solving a class of nonlinear fractional delay differential equations
Copyright policy )A new stable collocation method for solving a class of nonlinear fractional delay differential equations
AbstractIn 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.
- Harbin Institute of Technology China (People's Republic of)
nonlinear differential equations, \( \varepsilon \)-approximate solutions, Newton's iterative formula, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, fractional delay differential equations, Stability and convergence of numerical methods for ordinary differential equations, Functional-differential equations with fractional derivatives, Error bounds for numerical methods for ordinary differential equations
nonlinear differential equations, \( \varepsilon \)-approximate solutions, Newton's iterative formula, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, fractional delay differential equations, Stability and convergence of numerical methods for ordinary differential equations, Functional-differential equations with fractional derivatives, Error bounds for numerical methods for ordinary differential equations
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