MehrotraPredictorCorrectorTechnik

The Mehrotra Predictor-Corrector Technique is a numerical method used for solving systems of ordinary differential equations. It is a type of predictor-corrector method, meaning it involves two distinct steps: a prediction step and a correction step. This iterative approach aims to improve the accuracy of the solution over single-step methods like the Euler method.

In the prediction step, an initial estimate of the solution at the next time step is computed using a forward method, often a Runge-Kutta method of a certain order. This predicted value is then used in the correction step, where a different formula, typically an implicit one, is applied to refine the predicted value and obtain a more accurate approximation. The correction step often utilizes information from the current and predicted points to achieve higher accuracy.

The Mehrotra predictor-corrector technique is known for its ability to achieve higher accuracy than simpler methods for the same step size. It is particularly useful in situations where computational resources allow for the extra computations of the corrector step and where a higher degree of precision is required for the numerical solution. The specific formulas used in the prediction and correction phases can vary, leading to different orders of accuracy for the overall method. This technique is an advancement over basic predictor-corrector schemes by incorporating specific choices of predictor and corrector formulas designed for efficiency and accuracy.