In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation,
and is given by the formula
for Here, is the step size — a small positive number, and is the computed approximate value of The midpoint method is also known as the modified Euler method.
The name of the method comes from the fact that in the formula above the function is evaluated at which is the midpoint between at which the value of y(t) is known and at which the value of y(t) needs to be found.
The local error at each step of the midpoint method is of order, giving a global error of order . Thus, while more computationally intensive than Euler's method, the midpoint method generally gives more accurate results.
The method is an example of a class of higher-order methods known as Runge-Kutta methods.
Read more about Midpoint Method: Derivation of The Midpoint Method
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