Transforms Sturm-Liouville

Transforms in Finite Domain Sturm-Liouville Transforms 487... 

The strategy for using Sturm-Liouville transforms is, first, to carefully lay out the algebraic rules for this class of operator. Obviously, the defining equation and boundary conditions must be of the Sturm-Liouville type, as discussed in Chapter 10. 

Transforms in Finite Domain Sturm-Liouville Transforms 505 Substitution of Eq. 11.70 into Eqs. 11.67 to 11.69 yields... 

Transforms in Finite Domain Sturm-Liouville Transforms 515 forcing function (/-factor form). The methods from Chapter 2 show... 

To apply Sturm-Liouville transforms to coupled PDEs, we shall need to introduce a new concept function space. We introduce this methodology by way of a practical example batch adsorption in a vessel (Fig. 11.7). 

As we mentioned earlier, the fourth point of the development of this method is the inner product, which is the necessary ingredient to allow inversion. To obtain the inner product, just as in the case of Sturm-Liouville transform, we will start from the definition of the eigenproblem (Eqs. 11.195). 

In Chapters 7 to 12 we deal with numerical solution methods, and partial differential equations (PDE) are presented. Qassical techniques, such as combination of variables and separation of variables, are covered in detail. This is followed by Chapter 11 on PDE transform methods, culminating in the generalized Sturm-Liouville transform. This allows sets of PDEs to be solved as handily as algebraic sets. Approximate and numerical methods close out the treatment of PDEs in Chapter 12. 

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