Ordinary differential equations (ODEs) are also called initial value problems because a time zero value for each first-order differential equation is needed. The following is an example of a ...

The paper is intended to give a survey on the state-of-the-art of extrapolation methods for initial value problems in ordinary differential equation systems. All basic discretizations, which are ...

SIAM Journal on Numerical Analysis, Vol. 31, No. 4 (Aug., 1994), pp. 1147-1168 (22 pages) This work analyzes the integration of initial value problems for stiff systems of ordinary differential ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.