This book is suitable as a textbook for a first course on the Dynamic Relaxation technique in
civil and mechanical engineering curricula. It can be used as a reference by engineers and
scientists working in the industrial sector and in academic institutions. The first chapter
includes an introduction to the Dynamic Relaxation method (DR) which is combined with the
Finite Differences method (FD) for the sake of solving ordinary and partial differential
equations as a single equation or as a group of differential equations. In this chapter the
dynamic relaxation equations are transformed to artificial dynamic space by adding damping and
inertia effects. These are then expressed in finite difference form and the solution is
obtained through iterations. The procedural steps in solving differential equations using the
DR method were applied to the system of differential equations (i.e. ordinary and or partial
differential equations). The DR program performs the following operations: Reads data file
computes fictitious densities computes velocities and displacements checks stability of
numerical computations checks convergence of solution and checks wrong convergence. At the
end the Dynamic Relaxation numerical method coupled with the Finite Differences discretization
technique is used to solve nonlinear ordinary and partial differential equations. Subsequently
a FORTRAN program is developed to generate the numerical results as analytical and or exact
solutions.
