Heat Transfer in a Series of Tanks, dsolve

Example 2.9. Heat Transfer in a Series of Tanks, dsolve  

Warning, the protected names norm and trace have been redefined and unprotected 

We observe that solutions obtained for T2(t) and T3(t) using the dsolve command are long and messy compared to the solution obtained using the exponential matrix approach (Example 2.3). When more than three differential equations are to be solved it is recommended that the exponential matrix method be used. As an exercise, readers can verily that the solution obtained using the dsolve command is equivalent to the solution obtained in example 2.3. 

In this chapter anal5dical solutions were derived for linear ODEs using three methods the matrix exponential, Laplace transform, and dsolve. In section 2.1.2, 

Higher order ODEs (of order n) were converted to a system of n coupled linear first order ODEs in section 2.1.4. This system was then solved using the exponential matrix developed earlier. This approach yields analytical solutions for linear ODEs of any order. In section 2.1.5, the given system of coupled linear ODEs was converted to Laplace domain. The resulting linear system of algebraic equations was then solved for the solution in the Laplace domain. The solution obtained in the Laplace domain was then converted to the time domain. 

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