Toward Absolutely Stable Numerical Scheme

As a milestone for compatibility between the numerical stability and accuracy in numerical analysis for advection-diffusion equations this book presents third-order self-adaptive polynomial schemes to guarantee the nonnegativity condition for any computational conditions in both nonconservative form and conservative form by no means of flux limiters. As an application to advection equations the present scheme would be suggestive of a necessary and sufficient artificial viscosity to be locally ad...See More