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Natural SciencesMathematicsPhysicsComputational MechanicsComputational PhysicsDifferential EquationsContinuity EquationDifference EquationsFinite Difference MethodsNumerical Methods For Differential EquationsPartial Differential EquationsTime IntegrationConservation Law DiscretizationConservation LawsFinite Difference DiscretizationFinite Difference SchemesFinite Difference Solution Of Partial Differential Equations
Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.