借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软...借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。展开更多
Nonlinear Jacobi iteration and nonlinear Gauss-Seidel iteration are proposed to solve the famous Numerov finite difference scheme for nonlinear two-points boundary value problem. The concept of supersolutions and subs...Nonlinear Jacobi iteration and nonlinear Gauss-Seidel iteration are proposed to solve the famous Numerov finite difference scheme for nonlinear two-points boundary value problem. The concept of supersolutions and subsolutions for nonlinear algebraic systems are introduced. By taking such solutions as initial values, the above two iterations provide monotone sequences, which fend to the solutions of Numerov scheme at geometric convergence rates. The global existence and uniqueness of solution of Numerov scheme are discussed also. The numerical results show the advantages of these two iterations.展开更多
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ...Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.展开更多
文摘借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。
文摘Nonlinear Jacobi iteration and nonlinear Gauss-Seidel iteration are proposed to solve the famous Numerov finite difference scheme for nonlinear two-points boundary value problem. The concept of supersolutions and subsolutions for nonlinear algebraic systems are introduced. By taking such solutions as initial values, the above two iterations provide monotone sequences, which fend to the solutions of Numerov scheme at geometric convergence rates. The global existence and uniqueness of solution of Numerov scheme are discussed also. The numerical results show the advantages of these two iterations.
基金Supported by the Natural Science Foundation of Hunan Province（06JJ50008） Supported by the Natural Science Foundation of Guangdong Province（7004569）
文摘Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper.
