CH202 - Euler’s Explicit Formula Using Adaptive Step - Mathematics Assignment Help

Assignment Task -

1. Consider the following network of irreversible reactions occurring in a well mixed batch reactor: 

A →!"B →!#C →!$D 

Assuming that the initial concentration of species A is 1 mol/m3 and that of all other species  is 0 mol/m3, and values of rate constants k1, k2, and k3 are 1, 0.5, and 0.1 s-

 solve for the  concentrations of species A, B, C, and D from 0 to 50 seconds. For this, use an Euler’s  explicit formula using adaptive step size control. Plot the concentrations of all species on  the same plot (primary y axis), and the step size, h, used for each iteration on the same  plot (secondary y axis). Use the value for acceptable error, ε = 0.01. 

2. Now, consider that the part of the reaction where A produces B produces C  remains unchanged, but C reacts to produce D with a different kinetic rate expression

Now solve for the concentrations of all species as a function of time using Euler’s Implicit  formula. Note that you will have to solve a set of nonlinear algebraic equations at each  time iteration. Use the Matlab function fsolve for this. DO NOT write an adaptive step size  control algorithm here but use the step sizes that were obtained in Part 1, i.e. step sizes  will change with time, but you can directly use the changing step sizes obtained in Part

3. Now go back to the set of equations in Part 1 with first order kinetics. Assume  now that k1, k2, and k3 = 1s-1, so the system is no longer stiff.

Assume that these reactions are taking place in a square domain, where molecules can  move around by diffusion only (no convection). The species A enters the domain through  the left vertical edge and the reaction proceeds. All other edges are sealed, so there is no  flux through them. The boundary conditions and initial conditions are denoted in the figure below.

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