Numerical Methods For Conservation Laws From Analysis To Algorithms

This is not a first book on numerical methods. You need:

: Traditional "strong" solutions require the existence of derivatives. To account for shocks, mathematicians use the integral form of the equations to define "weak" solutions that can handle jumps in value. This is not a first book on numerical methods

Ujn+1=Ujn−ΔtΔx(Fj+1/2−Fj−1/2)cap U sub j raised to the n plus 1 power equals cap U sub j to the n-th power minus the fraction with numerator delta t and denominator delta x end-fraction open paren cap F sub j plus 1 / 2 end-sub minus cap F sub j minus 1 / 2 end-sub close paren This is not a first book on numerical methods

Conservation laws are the bedrock of mathematical physics and engineering. Whether we are modeling the flow of air over an aircraft wing (Euler equations), the traffic on a highway (Lighthill-Whitham-Richards model), or the propagation of a shock wave from an explosion, we are dealing with partial differential equations (PDEs) of the form: This is not a first book on numerical methods