|
In mathematics, the semi-implicit Euler method, also called symplectic Euler, semi-explicit Euler, Euler–Cromer, and Newton–Størmer–Verlet (NSV), is a modification of the Euler method for solving Hamilton's equations, a system of ordinary differential equations that arises in classical mechanics. It is a symplectic integrator and hence it yields better results than the standard Euler method. == Setting == The semi-implicit Euler method can be applied to a pair of differential equations of the form : : where ''f'' and ''g'' are given functions. Here, ''x'' and ''v'' may be either scalars or vectors. The equations of motion in Hamiltonian mechanics take this form if the Hamiltonian is of the form : The differential equations are to be solved with the initial condition : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Semi-implicit Euler method」の詳細全文を読む スポンサード リンク
|