A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The meth...A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The method is found to have a truncation error of O(h 6)and converges to the exact solution at O(h 4).The numerical examples show that our method is very effective and the maximum absolute error is acceptable.展开更多
We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asym...We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asymptotic expansion of a solution is uniformly valid on a finit interval. Meanwhile, we find an intrinsic relation between a solution of Riccati equations in the technique of diagnolization and an invariant manifold a boundary layer.MSC: 34E15展开更多
We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whol...We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.展开更多
This article shows the existence and asymptotic estimates of solutions of singularly perturbed boundary value problems for a class of third order nonlinear differential equations εx'' = f(t,x,x',ε), x(0)...This article shows the existence and asymptotic estimates of solutions of singularly perturbed boundary value problems for a class of third order nonlinear differential equations εx'' = f(t,x,x',ε), x(0) = A, x'(0) = x'(1), x'(0) = x'(1).展开更多
In this paper, the boundary value problem for the integro-differential equation with a small parameter ε>0:is discussed, where T'is are integral operators defined on C[0,1]:Using the differential inequality te...In this paper, the boundary value problem for the integro-differential equation with a small parameter ε>0:is discussed, where T'is are integral operators defined on C[0,1]:Using the differential inequality technique, the existence of solutions is proved and the estimate of solutions is obtained as well. In particular, this result applied to the high-order (n≥3) boundary value problem for ordinary differential equations with a small parameter ε>0:展开更多
In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behavio...In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently.展开更多
文摘A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The method is found to have a truncation error of O(h 6)and converges to the exact solution at O(h 4).The numerical examples show that our method is very effective and the maximum absolute error is acceptable.
文摘We study the boundary value problem for the vector system which is equivalent to a singular singularly-perturbed boundary value problem involving a slow variable. Under appropriate assumptions, we obtain that the asymptotic expansion of a solution is uniformly valid on a finit interval. Meanwhile, we find an intrinsic relation between a solution of Riccati equations in the technique of diagnolization and an invariant manifold a boundary layer.MSC: 34E15
基金Supported by the National Natural Science Foundation of China (No 10471039)the Natural Science Foundation of Zhejiang (No Y604127)Zhejiang Education Office (No 20030594)
基金Foundation item: Supported by Important Study Project of the National Natural Science Foundation of China (No. 90211004) and the Natural Science Foundation of Zhejiang (No. 102009).
文摘We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.
文摘This article shows the existence and asymptotic estimates of solutions of singularly perturbed boundary value problems for a class of third order nonlinear differential equations εx'' = f(t,x,x',ε), x(0) = A, x'(0) = x'(1), x'(0) = x'(1).
文摘In this paper, the boundary value problem for the integro-differential equation with a small parameter ε>0:is discussed, where T'is are integral operators defined on C[0,1]:Using the differential inequality technique, the existence of solutions is proved and the estimate of solutions is obtained as well. In particular, this result applied to the high-order (n≥3) boundary value problem for ordinary differential equations with a small parameter ε>0:
基金Supported by the National Natural Science Foundation of China (No.10471039)the Natural Science Foundations of Zhejiang (No.Y604127)the Zhejiang Eduction Office (No.20030594)the Natural Foundation of Huzhou Teacher's College (No.200302).
文摘In this paper, using the layer theory, a class of singularly perturbed Robin problem of nonlinear non-autonomous equation is considered. According to the different regions of the boundary value, the asymptotic behaviors of solution for the original problem are obtained simply and conveniently.
基金National Laboratory of BiomacromoleculesInstitute of Biophysics+3 种基金Chinese Academy of SciencesRFBR(09-01-00170)上海市自然科学基金(10ZR1409200)国家自然科学基金(11071075)
