The Application Of The Laplace Transform In The Heat Equation

Ana Uzla BatuBara

International Journal of Health, Engineering and Technology
Vol. 1 No. 6 (2023): IJHET-MARCH 2023

The one dimensional of homogeneous heat equation is two ordinary partial differential equations which general form , so needs solution. The one dimensional of homogeneous heat equation the method is ever been solved by Fourier series and Fourier Integrals. The other method used to in solving one dimensional of homogeneous heat equation is Laplace Transform, which is used to transform into ordinary differential equation is one dimension  for initial conditions . Inverse general solution that satisfies boundary conditions  is found, for every t and initial conditions  that have been transform is . From the result, it an obtain temperature on the poin x in the solid at time t.