Add support for Backwards Euler integration method · MatthewPeterKelly/OptimTraj#47

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good first issue

説明

One key feature in OptimTraj is the ability to compare different collocation methods. There is currently support for Hermite--Simpson collocation and trapezoidal collocation, as well as 4th-Order Runge--Kutta multiple shooting. It would be nice to add support for additional methods, and an good next step would be Backwards Euler collocation.

This feature could be implemented by copy-pasting the trapezoid.m file and switching it over to use backwards Euler](https://en.wikipedia.org/wiki/Backward_Euler_method) integration. The might be a few other details to work out, such as adding support to the top-level interfaces for the new method and also adding an example to show how to use the new method.

コントリビューターガイド

技術スタック: なし
領域: backend
Issue 種別: feature
難度: 2
推定時間: 1-3 hours
活動状況: fresh
明確さ: clear
前提条件: Basic MATLAB knowledgeUnderstanding of numerical integration
初心者向け度: 75
調査方針: The implementation can be done by copying the trapezoid.m file, modifying the integration scheme to use backward Euler as described in the Wikipedia link. Then, update the top level interfaces to include the new method and add an example script demonstrating its usage. Ensure that the new method is consistent with the existing collocation methods.