An iterative scaling function procedure for solving scalar non-linear hyperbolic balance laws
نویسندگان
چکیده
The scaling of the exact solution a hyperbolic balance law generates family scaled problems in which source term does not depend on current solution. These are used to construct sequence solutions whose limiting function solves original problem. Thus this gives rise an iterative procedure. Its convergence is demonstrated both theoretically and analytically. analytical demonstration terms local time existence theorem L2 framework for class s(q) bounded, with s(0)=0, locally Lipschitz belongs C2(R)?H1(R). A convex flux function, usual uniqueness conservation laws, also needed. For numerical demonstration, set model equations solved, where conservative finite volume method using low-dissipation implemented iteration stages. error against reference computed compared accuracy two conventional first order schemes assess gaining present Regarding only scheme explored because development useful procedure interest work, high-order accurate methods should increase computational cost global Numerical tests show that approach feasible
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ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 2021
ISSN: ['1873-5460', '0168-9274']
DOI: https://doi.org/10.1016/j.apnum.2020.12.009