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单词 Euler’s method
释义
Euler’s method

Mathematics
  • A simple numerical method for solving differential equations. If dydx=f(x,y) and an initial condition is known, y = y0 when x = x0, then Euler’s method generates a succession of approximations yn + 1 = yn + hf(xn,yn) where xn = x0 + nh, n ≥ 1. This takes the known starting point and moves along a straight line segment with horizontal distance h in the direction of the tangent at (x0,y0). The process is repeated from the new point (x1,y1) etc. If the step length h is small enough, the tangents are good approximations to the curve and the method will provide a reasonable accurate estimate. Compare Runge-Kutta methods.


Computer
  • See discretization.


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