This paper is concerned with obtaining the approximate solution for Volterra- Hammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function w（x） = 1 as ...This paper is concerned with obtaining the approximate solution for Volterra- Hammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function w（x） = 1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L^∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.展开更多
本文利用上下解方法研究了一般的二阶Volterra-Hammerstein型积分微分方程非线性边值问题 u″=f(t,u,T_1u,T_2u,u′),L(u(0),u′(0))=0,R(u(1),u′(1))=0, [T_1u](t)=φ_1(t)+integral from n=0 to t(K_1(t,s)u(s)ds),[T_2u](t)=φ_2(t)...本文利用上下解方法研究了一般的二阶Volterra-Hammerstein型积分微分方程非线性边值问题 u″=f(t,u,T_1u,T_2u,u′),L(u(0),u′(0))=0,R(u(1),u′(1))=0, [T_1u](t)=φ_1(t)+integral from n=0 to t(K_1(t,s)u(s)ds),[T_2u](t)=φ_2(t)+integral from n=0 to 1(K_2(t,s)u(s)ds),给出了解的存在性定理.展开更多
In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operator...In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operators, by means of upper and lower solutions method.展开更多
基金supported by National Natural Science Foundation of China(11401347,91430104,11671157,61401255,11426193)Shandong Province Natural Science Foundation(ZR2014AP003)
文摘This paper is concerned with obtaining the approximate solution for Volterra- Hammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function w（x） = 1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L^∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method.
文摘本文利用上下解方法研究了一般的二阶Volterra-Hammerstein型积分微分方程非线性边值问题 u″=f(t,u,T_1u,T_2u,u′),L(u(0),u′(0))=0,R(u(1),u′(1))=0, [T_1u](t)=φ_1(t)+integral from n=0 to t(K_1(t,s)u(s)ds),[T_2u](t)=φ_2(t)+integral from n=0 to 1(K_2(t,s)u(s)ds),给出了解的存在性定理.
文摘In this paper, we obtain the existence and uniqueness of solutions for nonlinear boundary value problem s of the form v″= f(l,v,v′,T′v,T1v,T2v), v(0) = A, g(v(1),v'(1)) = 0with Volterra and Hammerstein operators, by means of upper and lower solutions method.
