Transform Methods for Linear PDEs

In the previous chapters, partial differential equations with finite space domain were treated by the method of separation of variables. Certain conditions must be satisfied before this method could yield practical results. We can summarize these conditions as follows  

One independent variable must have a finite domain. 

The boundary conditions must be homogeneous for at least one independent variable. 

The resulting ODEs must be solvable, preferably in analytical form. 

With reference to item (4), quite often the ODEs generated by separation of variables do not produce easy analytical solutions. Under such conditions, it may be easier to solve the PDE by approximate or numerical methods, such as the orthogonal collocation technique, which is presented in Chapter 12. Also, the separation of variables technique does not easily cope with coupled PDE, or simultaneous equations in general. For such circumstances, transform methods have had great success, notably the Laplace transform. Other transform methods are possible, as we show in the present chapter. 

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Chapter 11 Transform Methods for Linear PDEs since it is easy to see... 

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