NS  Vol.5 No.4 , April 2013
Solution of non-linear boundary value problems in immobilized glucoamylase kinetics
ABSTRACT

A mathematical model to describe the enzyme reaction, mass transfer and heat effects in the calorimetric system is discussed. The model is based on non-stationary diffusion Equation containing a nonlinear term related to immobilize liver esterase by flow calorimetry. This paper presents the complex numerical methods (Adomian decomposition method, Homotopy analysis and perturbation method) to solve the non-linear differential Equations that depict the diffusion coupled with a non-linear reaction terms. Approximate analytical expressions for substrate concentration have been derived for all values of parameters α, β and γE. These analytical results are compared with the available numerical results and are found to be in good agreement.


Cite this paper
Sevukaperumal, S. , Eswari, A. and Rajendran, L. (2013) Solution of non-linear boundary value problems in immobilized glucoamylase kinetics. Natural Science, 5, 478-494. doi: 10.4236/ns.2013.54061.
References
[1]   Monk, P. and Wadso, I. (1968) A flow micro reaction. Acta Chemica Scandinavica, 22, 1842-1852. doi:10.3891/acta.chem.scand.22-1842

[2]   Burch, J. (1954) The purification and properties of horse liver esterase. Biochemistry, 58, 415-426.

[3]   Stoops, J.K., Horgan, D.J., Runnegar, M.T.C., Jersey, J., dewebb, E.C. and Zerner, B. (1969) Carboxylesterases (EC 3.1.1). Kinetic Studies on Carboxylesterases Biochemistry, 8, 2026-33.

[4]   Adler, A.J. and Kistiakowasky, G.B. (1962) Kinetics of pig liver esterase catalysis. Journal of the American Chemical Society, 84, 695-703. doi:10.1021/ja00864a001

[5]   Stefuca, V., Gemenier, P. and Scheper, V., Eds. (1999) Advances in biochemical engineering biotechnology. Springer, Berlin, 71.

[6]   Stefuca, V., Vikartovska-Welwardova, V. and Gemenier, P. (1999) Flow microcalorimeter auto-calibration for the ana lysis of immobilized enzyme kinetics. Analytica Chimica Acta, 355, 63. doi:10.1016/S0003-2670(97)81612-1

[7]   Stefuca, V., Cipakova, I. and Gemeine, P. (2001) Investigation of immobilized glucoamy lase kinetics by flow calorimetry. Thermochimica Acta, 378, 79-85. doi:10.1016/S0040-6031(01)00589-5

[8]   Malik, F., Stefuca, V. and Bales, V. (2004) Investigation of kinetics of immobilized liver esterase by flow calorimetry. Journal of Molecular Catalysis B: Enzymatic, 29, 81-87. doi:10.1016/S0040-6031(01)00589-5

[9]   Jaradat, O.K. (2008) Adomian decomposition method for solving abelian differential equations. Journal of Applied Sciences, 8, 1962-1966. doi:10.1016/S0040-6031(01)00589-5

[10]   Majid Wazwaz, A. and Gorguis, A. (2004) The decomposition method applied to systems of partial differential equations. Applied Mathematics and Computation, 149, 807-814.

[11]   Makinde, O.D. (2007) Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy. Applied Mathematics and Computation, 184, 842-848. doi:10.1016/j.amc.2006.06.074

[12]   Siddiqui, A.M., Hameed, M., Siddiqui, B.M. and Ghori, Q.K. (2010) Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid. Communications in Nonlinear Science and Numerical Simulation, 15, 2388-2399. doi:10.1016/j.cnsns.2009.05.073

[13]   Mohamed, M.A. (2010) Comparison differential trans formation technique with Adomian decomposition method for dispersive long-wave equations in (2+1)-dimensions. Applied Mathematics, 5, 148-166.

[14]   Liao, S.J. (1992) The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D. The sis, Shanghai Jiao Tong University, Shanghai.

[15]   Liao, S.J. (2003) Beyond perturbation: Introduction to the homotopy analysis method. CRC Press, Boca Raton. doi:10.1201/9780203491164

[16]   Awaadeh, F., Jaradat, H.M. and Alsyyed, O. (2009) Analytical solution for nonlinear gas dynamic equation by homotopy analysis method. Chaos, Solitons & Fractals, 42, 1422-1427.

[17]   Jafari, H., Chun, C. and Saeidy, S. (2009) Analytical solution for nonlinear gas dynamic equation by homotopy analysis method. Applied Mathematics, 4, 149-154.

[18]   Sohouli, A.R., Famouri, M., Kimiaeifar, A. and Domairry, G. (2010) Application of homotopy analysis method for natural convection of Darcian fluid about a vertical full cone embedded in pours media prescribed surface heat flux. Communications in Nonlinear Science and Numerical Simulation, 15, 1691-1999. doi:10.1016/j.cnsns.2009.07.015

[19]   Domarriy, G. and Fazeli, M. (2009) Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Communications in Nonlinear Science and Numerical Simulation, 14, 489-499. doi:10.1016/j.cnsns.2007.09.007

[20]   Liao, S.J. (2004) On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147, 499-513. doi:10.1016/S0096-3003(02)00790-7

[21]   Domairry, G. and Barring, H. (2008) An approximation of the analytic solution of some nonlinear heat transfer equations: A survey by using homotopy analysis method. Ad vanced Studies in Theoretical Physics, 2, 507-518.

[22]   He, J.H. (2000) A coupling method of homotopy tech nique and a perturbation technique for non-linear problems. International Journal of Non-Linear Mechanics, 35, 37-43. doi:10.1016/S0020-7462(98)00085-7

[23]   Ganji, D.D., Amini, M. and Kolahdooz, A. (2008) Ana lytical investigation of hyperbolic equations via He’s methods. American Journal of Engineering and Applied Sciences, 1, 399-407. doi:10.3844/ajeassp.2008.399.407

[24]   Ariel, P.D. (2010) Homotopy perumbation method and natural convention flow of a third grade fluid through a circular tubenon. Nonlinear Science Letters A, 1, 43-52.

[25]   Fereidoon, A., Rostamiyan, Y., Davoudabadi, M.R., Farahani, S.D. and Ganji, D.D. (2010) Analytic approach to investigation of distributions of stresses and radial displacement at the thick-wall cylinder under the internal and external pressures. Middle-East Journal of Scientific Research, 5, 321-328.

 
 
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