Approximate solution of a nonlinear partial differential equation


Vajta, M. (2007) Approximate solution of a nonlinear partial differential equation. In: Mediterranean Conference on Control & Automation, 27-29 June 2007, Athens, Greece (pp. T23 033).

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Abstract:Nonlinear partial differential equations (PDE) are notorious to solve. In only a limited number of cases can we find an analytic solution. In most cases, we can only apply some numerical scheme to simulate the process described by a nonlinear PDE. Therefore, approximate solutions are important for they may provide more insight about the process and its properties (stability, sensitivity etc.). The paper investigates the transient solution of a second order, nonlinear parabolic partial differential equation with given boundary- and initial conditions. The PDE may describe various physical processes, but we interpret it as a thermal process with exponential source term. We develop an analytical approximation, which describes the inverse solution. Accuracy and feasibility will be demonstrated. We also provide an expression for the time-derivative of the transient at time zero. The results can be extended for other boundary conditions as well.
Item Type:Conference or Workshop Item
Copyright:© 2007 IEEE
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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