CONCLUSION
Partial differential equation has a lot of application to real world systems. This research attempted to discuss the applications second-order partial differential equation by using modeling phenomenon of real life problems. Some of the models include diffusion of heat, vibration of string.
Mathematically, it is possible to present the conduction of heat to some extent of accuracy by using the Fourier series and separation of variables techniques which is represented by second order differential equation.
Second order partial differential equation can be used to explain analytically the heat equations, wave equations. From this discussion we get some ideas of how partial differential equations are connected with physical applications and how natural relationship in different field of science is put together in terms of partial differential equation.
Physical problems motivated the development of applied mathematics which is true for partial differential equations that have helped to solve real life problems in the field. It has made the study and status of pde essential in this regard.
As a conclusion, many fundamental problems in biology, physical science and engineering are described by partial differential equations. It is believed that many unsolved problems in future technologies will be solved using partial differential equation.
