Approximate solution of a nonlinear partial differential equation

Miklos Vajta

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    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.
    Original languageEnglish
    Title of host publicationProceedings of the 2007 Mediterranean Conference on Control and Automation
    Place of PublicationPiscataway, NJ
    PagesT23 033
    Number of pages5
    ISBN (Print)1-4244-1282-X
    Publication statusPublished - 2007
    Event15th Mediterranean Conference on Control & Automation, MED 2007 - Athens, Greece
    Duration: 27 Jun 200729 Jun 2007
    Conference number: 15


    Conference15th Mediterranean Conference on Control & Automation, MED 2007
    Abbreviated titleMED


    • MSC-93C20
    • Distributed parameter systems
    • Partial differential equations
    • Heat processes
    • Approximations


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