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Question

2. In the battle of Trafalgar in 1805, we saw that if the two forces simply engaged head-on, the British lost the battle and approximately 24 ships, whereas the French-Spanish force lost approximately 15 ships. We also saw that Lord Nelson could overcome a superior force by employing a divide-and-conquer strategy. An alternative strategy for overcoming a superior force is to increase the technology employed by the inferior force. Suppose that the British ships were equipped with superior weaponry, and that the French-Spanish suffered losses equal to 15% of the number of ships of the opposing force, whereas the British suffered casualties equal to 5% of the opposing force.

a) Formulate a system of difference equations to model the number of ships possessed by each force. Assume the French-Spanish start with 33 ships and the British start with 27 ships.
b) Build a numerical solution to determine who wins under new assumption in a head-on engagement.
c) Build a numerical solution for the three battles employing Nelson’s divide-and-conquer strategy coupled with the superior weaponry of the British ships.

Answer 1

2. 在特拉法尔加战役在1805年，我们看到，如果仅仅两股力量从事正面，英国失去了战斗，大约24船，而法国和西班牙部队损失了大约15船。我们还看到，纳尔逊勋爵可以克服上级武力雇用分而治之的策略。另一种战略，克服了优势兵力是增加雇用的技术劣势生效。假设英国船只配备了卓越的武器，并说，法国和西班牙遭受损失等于15 ％的船舶数目的反对力量，而英国遭受伤亡等于5 ％的反对力量。
a ）制定系统的差分方程模型的船舶数目所拥有的每一个部队。假设法国与西班牙启动33船舶和英国27日开始的船只。
b ）建立一个数值的解决方案，以确定谁胜根据新的假设在正面接触。

。在特拉法尔加战役在1805年，我们看到，如果仅仅两股力量从事正面，英国失去了战斗，大约24船，而法国和西班牙部队损失了大约15船。我们还看到，纳尔逊勋爵可以克服上级武力雇用分而治之的策略。另一种战略，克服了优势兵力是增加雇用的技术劣势生效。假设英国船只配备了卓越的武器装备，法国和西班牙遭受损失等於15 ％的船舶数目的反对力量，而英国遭受伤亡等於5 ％的反对力量。

a ）制定系统的差分方程模型的船舶数目所拥有的每一个部队。假设法国与西班牙启动33船舶和英国27日开始的船只。
b ）建立一个数值的解决方案，以确定谁胜根据新的假设在正面接触。
c ）建立了数值解的三个战役雇用尼尔森的分而治之的战略加上优势装备的英国船只。