| Summary: | 碩士 === 靜宜大學 === 應用數學研究所 === 93 === Mainly is the square distance that solves the differential equation with Lie symmetry method . Lie symmetry to provide a set of systematic method, making the differential equation reached the purpose of Reduction of Order.
While usually using the square distance of the standard method solution differential equation, sometimes too in comlications, hence think of then with Lie symmetry method. Make to solve under the certain condition more simple and direct .We is symmetry by Lie in solving a order often the square distance of the differential calculus of to some inspire, and apply in high level of often the square distance of the differential equations.By generator Lie symmetry basis, we can make use that the canonical coordinates transformation reduces the order gradually then .With reach the power of reducing the square distance, make square distance better solve.Also compared to solve the difference of the square distance of the differential equation with the standard method, let to solve the square distance to have another a kind of choice.
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