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|Runge-Kutta Methods||These are classical methods for solving ordinary differential equations numerically. The main problem with Euler's method is that to get a reasonably accurate result, one has to use a small interval size. As a result, it is not that efficient. The Runge-Kutta method is an upgrade. It produces better results in fewer steps. These methods use the data on the slope at multiple points to extrapolate the solution to the future time step. Runge-Kutta methods are explicit. For this reason, they are only conditionally stable.|
|Euler’s method||Although there are many ways of solving differential equations, sometimes these methods fail or are too complicated to be solved by hand. Euler's method can be used when there is a condition that will work when other methods fail. We can define it as one of the techniques used to evaluate differential equations that are based on the idea of local linearity or linear estimation. In this method, small tangent lines are used over short distances to estimate the solution to an initial-value problem.|
|Hamming method||This method is named after Richard Wesley Hamming, the mathematician who invented it in 1959. The Hamming method is a powerful technique extensively used for uncertain ordinary differential equations. It is a stable predictor-corrector method used to approximate solutions of the initial-value problem over an interval. The Hamming method is considered the most effective compared to the other techniques mentioned here.|
|Midpoint method||Also known as the second-order Runge-Kutta method, the midpoint method is an improvement of the Euler’s technique. It increases the accuracy by one order by adding a midpoint in the step. Send us a “complete my ordinary differential equations assignment if you are not acquainted with any of these techniques.|
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