Lie Symmetry Analysis on Fujita Storm Equation

Tan, Kar Cheng (2018) Lie Symmetry Analysis on Fujita Storm Equation. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

Partial differential equations occur and used to describe real physical situation. However, not all the partial differential equation can be solved by using same method especially for the equation that consists of nonlinearity. Lie symmetry analysis would be one of the methods that used to solve nonlinear partial differential equation. Unlike numerical method, Lie symmetry analysis provides an exact solution instead of numerical solution. Solution of the partial differential equation is useful for the researchers to understand the problem and carry out more investigations about the equation. Fujita- Storm Equation, which is a nonlinear partial differential equation is studied and solved using the Lie symmetry analysis method that introduced by Sophus Lie. Symmetries of the equation were used to transform the partial differential equation into ordinary differential equation which only consists of one variable. Reduction of the order is required because the first order ordinary differential equation is easier to solve. Solution of the Fujita- Storm equation will be useful for the researchers that studied on the soil hydrology. Since convective terms can be added into this equation and used for different purposes, solving this equation gives others an idea on how to solve the equation with convective terms.