Solutions For Mathematical Model Arising From Chemical And Electrochemical Reaction Engineering By Adomian Decomposition Method

A new method for computing initial values for a class of special boundary value problems of second order ordinary differential equations arising from the mathematical model of chemical and electrochemical reaction engineering is given. Three mathematical models for porous catalyst and porous electrode are solved concretely and for different values of parameters the graphs of their solutions are depicted. Comparing with traditional shooting method this method avoid the complex iterative operation and only need solving an equation using dichotomy satisfied by initial value which is expressed by a variable upper limit function. Based on the high precision of computing the generalized integral using MATLAB the initial values determined by this method are also of high precision. In addition, these models are also solved by using Adomian decomposition. The computing results of these two methods show that the convergence rates of the infinite series obtained by expanding the nonlinear term in the equation into Adomian polynomials greatly impact the convergence rates of approximate analytic solution for the equation.A system of second-order partial differential equations with nonstandard boundary conditions is solved. This system of equations is a mathematical model that describes distributions of the overpotential and reactant concentration in a working packed-bed electrode for an electrochemical reactor. To ensure the existence and uniqueness of the solutions for this model we choose the direction in which standard instead of non-standard boundary conditions is, and obtain approximate analytic solutions in the form of a series that rapidly converges using the Adomian decomposition method. The method is easily implemented using the symbol and numerical operations of MATLAB.A mathematical model of a packed-bed catalytic reactor, which is a system of second-order strong nonlinear partial differential equations with incompatible boundary conditions, will be solved. By properly using the boundary conditions and correctly choosing the solution search direction, approximate analytic solutions for the model can be obtained by the Adomian decomposition method. When the values of the dimensionless parameters in the system are assigned within a suitable range, the solutions describe objectively the distribution of temperature and the key reactant in the reactor.