Abstract
Problems like population growth, continuous stirred tank reactor (CSTR)
and ideal gas are studied from the last four decades in the field
medicine science, Engineering and applied science, respectively. One of
the main motivation was to understand the pattern of such issues and how
to fix them. With the help of applied Mathematics, such problems can be
converted or modeled by nonlinear expressions with similar properties
and the required solution can be obtained by iterative techniques. In
this manuscript, we proposed a new iterative scheme for multiple roots
(without prior knowledge of multiplicity m) by adopting
multiplicative calculus rather than the standard calculus. The base of
our scheme is on the well-known Schröder method and we retain the same
second-order of convergence. In addition, we extend the order of
convergence from second to fourth by constructing a two-step joint
Schröder scheme with hybrid approach of ordinary and multiplicative
calculus. Some numerical examples are tested to find the roots of
nonlinear equations and results are found to be competent as compared to
ordinary derivative methods. Finally, the convergence of schemes is also
analyzed by basin of attractions that also support the theoretical
aspects.