Using FEMLAB to Solve Ordinary Differential Equations

USING FEMLAB TO SOLVE ORDINARY DIFFERENTIAL EQUATIONS 

FEMLAB is treated in detail in Chapters 9-11 and Appendix D, but it can also be used to solve reactor problems. The advantage of FEMLAB is that you program with a GUI, so computer errors are less likely. It is still necessary to check your work, though. While the applications in this chapter are all one-dimensional (to compare with MATLAB solutions), it is easy to solve two-dimensional problems, as described in more detail in later chapters. We show here how to solve the same three problems already solved using MATLAB the simple exponential, Eq. (8.16) the isothermal flow reactor, Eqs. (8.21)—(8.22) and the nonisothermal reactor, Eqs. (8.24)-(8.26). 

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Using FEMLAB to solve ordinary differential equations. Chapter 8, p. 123. 

Packages to solve boundary value problems are available on the Internet. On the NIST web page http //gams.nist.gov/, choose problem decision tree and then differential and integral equations and then ordinary differential equations and multipoint boundary value problems. On the Netlibweb site http //www.netlib.org/, search on boundary value problem. Any spreadsheet that has an iteration capability can be used with the finite difference method. Some packages for partial differential equations also have a capability for solving one-dimensional boundary value problems [e.g. Comsol Multiphysics (formerly FEMLAB)]. 

The differential equation, (1.2), is an ordinary differential equation because there is only one independent variable, x In this case, equations in one space dimension are boundary value problems, because the conditions are provided at two different locations. While it is also possible to solve this problem using Excel and MATLAB, it is much simpler to use FEMLAB. Transient heat transfer in one space dimension is governed by... 

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