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In this chapter, we shall deal with method-of-lines solutions to models that are described by individual partial differential equations, by sets of coupled partial differential equations, or possibly by sets of mixed partial and ordinary differential equations.
Emphasis will be placed on the process of converting partial differential equations to equivalent sets of ordinary differential equations, and particular attention will be devoted to the problem of converting boundary conditions. To this end, we shall again consult our -meanwhile well-understood-Newton-Gregory polynomials.
We shall then spend some time analyzing the particular difficulties that await us when numerically solving the sets of resulting differential equations in the cases of parabolic, hyperbolic, and elliptic partial differential equations. It turns out that each class of partial differential equations exhibits its own particular and peculiar types of difficulties.
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6.12 References
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6.13 Bibliography
Myron B. Allen, Ismael Herrera, and George F. Pinder. Numerical Modeling in Science and Engineering. John Wiley & Sons, New York, 1988. 418p.
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(2006). Partial Differential Equations. In: Continuous System Simulation. Springer, Boston, MA. https://doi.org/10.1007/0-387-30260-3_6
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