Technical report: solving heat equation by Lie algebra / Nur Adilla Rosezali, Syazana Noorshirwan and Norsyuhada Ruhani@Mohd Rosli

Differential equations are important in variety scientific fields. Usually, they are quite challenging to solve. In this project, a more universal method for solving differential equation is obtained compared to the familiar methods in solving ordinary and partial differential equation, (PDE). In this research, a method developed by Sophus Lie which uses groups of symmetries, called Lie Groups is applied in order to solve differential equation. The main problem in solving PDE is when it is in higher order and contains more than two independent variables involved which will contribute to high levels of difficulty. The purpose of this project is to obtain one­parameter infinitesimal transformation group and used it to transform heat equation. Lastly, the infinitesimal transformation will be apply to find the exact solution of heat equation. The calculation of the derivatives that will be used in finding the exact solution of heat equation will be explain in detailed. In future, Lie algebra can be apply to solve higher order partial differential equation that contains more than two independent variables.