An Approximate Proximal Numerical Procedure Concerning the Generalized Method of Lines
Fabio Botelho
Abstract
This article develops an approximate proximal approach for the generalized method of lines. We recall that for the generalized method of lines, the domain of the partial differential equation in question is discretized in lines (or in curves) and the concerning solution is developed on these lines, as functions of the boundary conditions and the domain boundary shape. Considering such a context, in the text we develop an approximate numerical procedure of proximal nature applicable to a large class of models in physics and engineering. Finally, in the last sections, we present numerical examples and results related to a Ginzburg–Landau-type equation.
Topics & Concepts
DiscretizationMethod of linesPartial differential equationDomain (mathematical analysis)MathematicsContext (archaeology)Boundary value problemBoundary (topology)Class (philosophy)Numerical analysisMathematical analysisApplied mathematicsDifferential equationComputer scienceOrdinary differential equationBiologyArtificial intelligenceDifferential algebraic equationPaleontologyAdvanced Numerical Analysis TechniquesNumerical methods for differential equationsIterative Methods for Nonlinear Equations