摘要：In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods;the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme;they are shown to satisfy the criteria for both consistency and stability;hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.

摘要：财富、名声、权力、地位皆可追求,人们也无时无刻不在追求,而我们的确可能达成这类目标。但若以财名权位为惟一目标,反而难以如愿。因为这几项事物,通常是达到其他目标所带来的副产品。例如,足球选手因脚程飞快而致富;商人因创业有成而闻名;舞者因艺术成就,而在表演艺术圈内取得权力;志愿工作人员因致力扫除贫困,或照顾流浪无依人士等善行,而取得崇高的社会地位。财富、名声、权力、地位有时是成功带来的后果,然后又可反过来扩充成功的规模,提升其层次,扩大其影响层面;但财权地位从来就不是成功的本质。因此,一味追逐这些东西,实在是搞错了目标。我们的成功观应该与我们对“卓越”“、成就”乃至“快乐”的概念更密切关联。仔细环