A procedure is examined which solves systems of linear differential equations by quadratures. A direct check shows that a necessary condition for the procedure cannot be true and hence the procedure does not work.

A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy. Consider the Dirac equation of an electron

Abstract Mimetic finite difference operators $$\textbf{D}$$ D , $$\textbf{G}$$ G are discrete analogs of the continuous divergence (div) and gradient (grad) operators. In sense, these satisfy same properties as those their continuum counterparts. particular, they a extended Gauss’ theorem. Th...

them particularly important in solvinG physical problems. Also, Gaussian integration provides a highly accurate and efficient algorithm for integrating functions. The value of the methods I describe in this installment of “Computing Prescriptions” depends on the basic assumption that a finite-order polynomial can effectively approximate a function. Therefore, a finite sum of orthogonal polynomi...