The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form By constructing a Lyapunov functional, s...The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form By constructing a Lyapunov functional, sufficient conditions for the stability of the zero solution of this equation are established.展开更多
A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization tech...A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques.展开更多
In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results i...In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results in[3].AMS Classification numbers:34D20,34D99展开更多
We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The ac...We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions.展开更多
In this paper, we discuss the instability of the zero solutions to certain nonlinear differential equations of fifth and sixth order with multiple retarded arguments. By the Lyapunov's direct method, sufficient condi...In this paper, we discuss the instability of the zero solutions to certain nonlinear differential equations of fifth and sixth order with multiple retarded arguments. By the Lyapunov's direct method, sufficient conditions for instability of the zero solutions are obtained.展开更多
文摘The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form By constructing a Lyapunov functional, sufficient conditions for the stability of the zero solution of this equation are established.
文摘A numerical method based on septic B-spline function is presented for the solution of linear and nonlinear fifth-order boundary value problems. The method is fourth order convergent. We use the quesilinearization technique to reduce the nonlinear problems to linear problems and use B-spline collocation method, which leads to a seven nonzero bands linear system. Illustrative example is included to demonstrate the validity and applicability of the proposed techniques.
文摘In this paper,we show the asymptotic stability in the large of the trivial solution x 0 for case p=0 and the boundedness result of solutions(1.1) for case p≠0.The resultobtained here extend the author's results in[3].AMS Classification numbers:34D20,34D99
文摘We use fifth order B-spline functions to construct the numerical method for solving singularly perturbed boundary value problems. We use B-spline collocation method, which leads to a tri-diagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical results are found in good agreement with exact solutions.
文摘In this paper, we discuss the instability of the zero solutions to certain nonlinear differential equations of fifth and sixth order with multiple retarded arguments. By the Lyapunov's direct method, sufficient conditions for instability of the zero solutions are obtained.