  In this paper, we develop a stable and fast numerical scheme for relativistic
dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory
is a stable and causal description of dissipation in relativistic hydrodynamics
although it includes relaxation process with the timescale for collision of
constituent particles, which introduces stiff equations and makes practical
numerical calculation difficult. In our new scheme, we use Strang's splitting
method, and use the piecewise exact solutions for solving the extremely short
timescale problem. In addition, since we split the calculations into inviscid
step and dissipative step, Riemann solver can be used for obtaining numerical
flux for the inviscid step. The use of Riemann solver enables us to capture
shocks very accurately. Simple numerical examples are shown. The present scheme
can be applied to various high energy phenomena of astrophysics and nuclear
physics.

High Energy Astrophysical Phenomena;Instrumentation and Methods for Astrophysics;Nuclear Theory;Computational Physics;Fluid Dynamics;Plasma Physics