A mathematical study on non-linear initial-boundary value problem for R-D equation

Vembu Ananthaswamy; J. Chitra; J. Anantha Jothi; Seenith Sivasundaram

Vembu Ananthaswamy The Madura College, Madurai, Tamil Nadu, India.
J. Chitra Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India
J. Anantha Jothi Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.
Seenith Sivasundaram College of Science, Engineering and Mathematics, Daytona Beach, Florida 321114, USA

Abstract

A mathematical modelling of cubic autocatalytic reactions with precursor chemicals and linear decay are studied. The model is associated with the diffusion, which is treated in a 1-D reactor. In this model, reactants are delivered by two mechanisms: diffusion across the cell boundaries and degradation of precursor chemical abundant within the reactor. The semi analytical solutions are derived for the concentration of dimensionless reactant and dimensionless autocatalyst in the cubic autocatalytic reaction-diffusion equations for the time dependent and time independent by using the Homotopy analysis technique. The obtained semi analytical solutions are then compared with the numerical simulation and found to be very good fit for all values of the dimensionless parameters.