Abstract Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical to solve steady-state solutions hyperbolic partial differential equations (PDEs). The Gauss-Seidel iterations and alternating strategy used cover characteristics PDEs in each order achieve convergence rate solutions. A nice property fixed-point which distinguishes them from other is that they explicit ...

In everyday life human faces shock waves and rarefaction largely in their surroundings. Hence it’s necessary to know the behavior of these protect destructive effects. The aim this work observe propagation various dynamics due solve non-linear hyperbolic inviscid Burgers’ equation numerically. models adopted here two numerical schemes which enable us first order explicit upwind scheme (EUDS) se...

Discrete updates of numerical partial differential equations (PDEs) rely on two branches temporal integration. The first branch is the widely-adopted, traditionally popular approach method-of-lines (MOL) formulation, in which multi-stage Runge-Kutta (RK) methods have shown great success solving ordinary (ODEs) at high-order accuracy. clear separation between and spatial discretizations governin...

Compact Approximate Taylor (CAT) methods for systems of conservation laws were introduced by Carrillo and Pares in 2019. These methods, based on a strategy that allows one to extend high-order Lax-Wendroff nonlinear without using the Cauchy-Kovalevskaya procedure, have arbitrary even order accuracy 2p use (2p + 1)-point stencils, where p is an positive integer. More recently 2021 Carrillo, Macc...

the accurate estimation of reaeration rate coefficient, because of its effects on dissolved oxygen in rivers, is one of the most important initial steps of water quality management. the main goal of this paper is to evaluate the effects of reaeration rate coefficient on the river water dissolved oxygen, case study dinachal river, iran. to achieve these aims, water quality samples were collected...

A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum, and energy equations are solved by different methods. It especially designed here developing new discretizations of the total equation adapted a thermal coupling with lattice Boltzmann method (LBM). The proposed linear equivalence standard entropy e...

We show that a recently introduced Lax pair of the Sawada-Kotera equation is nota new one but is trivially related to the known old Lax pair. Using the so-called trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.