Euler's method

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The simplest numerical method for solving differential equations. If 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, 2, 3,…. 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. The method provides a reasonably accurate estimate.

Subjects: Mathematics.

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