r. ewing, o. liev, r. lazarov and a. naumovich in [1] proposed a finite volume discretization for one dimensional biot poroelasticity system in multilayer domains. their discretization and exact solution are invalid. we derive valid discretization and exact solution. finally, our numerical solution is compared with known exact solution in discrete l2 norm.

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

Let $$X_N$$ be an N-dimensional subspace of $$L_2$$ functions on a probability space $$(\Omega , \mu )$$ spanned by uniformly bounded Riesz basis $$\Phi _N$$ . Given integer $$1\le v\le N$$ and exponent p\le 2$$ we obtain universal discretization for the integral norms $$L_p(\Omega ,\mu from collection all subspaces v elements with number m required points satisfying $$m\ll v(\log N)^2(\log v)^...