We studied the morphological evolution during spinodal phase
separation and subsequent coarsening kinetics in systems with strong
dependence of elastic constants on composition.  An efficient
numerical method is developed for solving the inhomogeneous elasticity
equations by using the conjugate gradient method (CGM).  A simple
model binary system with a symmetric miscibility gap is considered.
It is shown that the early stages of spinodal phase separation in a
solid solution with a $50\%-50\%$ composition always results in
interconnected morphology, regardless of the degree of elastic
inhomogeneity.  For systems with strong elastic inhomogeneity,
particle splitting and coalescence take place concurrently during
coarsening in both elastically isotropic and anisotropic systems.  In
the late stages, the morphology has the characteristics that the hard
phase forms the precipitates surrounded by the soft phase which forms
the matrix, similar to that predicted by others using first-order
approximations. An analysis of the coarsening kinetics shows that
although the growth exponent decreases with the increase in the degree
of elastic inhomogeneity, there is no freezing of the coarsening
kinetics for all the cases that we studied, in contrast to that
predicted by some prior works.  The effect of an externally applied
strain on the two-phase morphology is discussed.