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The Numerical Method of Lines: Integration of Partial Differential Equations.
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1993
Year
Numerical AnalysisMethod Of Fundamental SolutionSpatial DifferentiationEngineeringNumerical ComputationAdaptive GridsNumerical SimulationNumerical MethodNumerical StabilityNumerical TreatmentNumerical MethodsBoundary Element MethodNumerical Method For Partial Differential Equation
The Numerical Method of Lines discretizes spatial variables in partial differential equations to transform them into systems of ordinary differential equations, enabling efficient numerical solutions across many scientific and engineering applications. The paper extends the Method of Lines to handle multidimensional partial differential equations and adaptive grid techniques. The authors detail spatial differentiation strategies, initial value integration procedures, stability considerations, and supply appendices containing Laplacian operators, differentiation routines, and a library of ODE/PDE applications. Index.
What Is the Numerical Method of Lines? Some Applications of the Numerical Method of Lines. Spatial Differentiation. Initial Value Integration. Stability of Numerical Method of Lines Approximations. Additional Applications: Multidimensional Pdes and Adaptive Grids. Appendix A: The Laplacian Operator in Various Coordinate Systems. Appendix B: Spatial Differentiation Routines. Appendix C: Library of ODE and ODE/PDE Applications. Index.