Nonlinear Laplace/Poisson Equation

  • Akpofure E. Taigbenu


In the previous chapter, we presented the boundary element and Green element formulations for the linear version of the steady 1-D. second-order differential equation given by eq. (2.1) in which the parameter K assumed a constant value. We used the example of flow in a confined aquifer of uniform thickness to derive the linear form of the differential equation. Here we relax that condition and consider cases where K is a function of the spatial variable x (heterogeneous case), and a function of the dependent variable h (nonlinear case). Nonlinear heterogeneous problems are frequently encountered in many engineering applications — heat flux through a material whose thermal properties are nonlinear, infiltration into unsaturated soils, elastic deformation of a bar of varying section subject to axial loads, etc. We elect to use a heat transfer example to derive the nonlinear equation of the form of eq. (2.1).


Boundary Element Green Element Element Equation Picard Scheme Dual Reciprocity Boundary Element Method 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Akpofure E. Taigbenu
    • 1
  1. 1.Department of Civil and Water EngineeringNational University of Science and TechnologyBulawayoZimbabwe

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