Skip to main content Accessibility help
  • This chapter is unavailable for purchase
  • Print publication year: 2010
  • Online publication date: June 2012

1 - Types and sources of numerical error



The job of a biomedical engineer often involves the task of formulating and solving mathematical equations that define, for example, the design criteria of biomedical equipment or a prosthetic organ or physiological/pathological processes occurring in the human body. Mathematics and engineering are inextricably linked. The types of equations that one may come across in various fields of engineering vary widely, but can be broadly categorized as: linear equations in one variable, linear equations with respect to multiple variables, nonlinear equations in one or more variables, linear and nonlinear ordinary differential equations, higher order differential equations of nth order, and integral equations. Not all mathematical equations are amenable to an analytical solution, i.e. a solution that gives an exact answer either as a number or as some function of the variables that define the problem. For example, the analytical solution for

(1) x2 + 2x + 1 = 0 is x = ±1, and

(2) dy/dx + 3x = 5, with initial conditions x = 0, y = 0, is y = 5x − 3x2/2.

Sometimes the analytical solution to a system of equations may be exceedingly difficult and time-consuming to obtain, or once obtained may be too complicated to provide insight.

Ali, M. M. and Vaidya, V. (2007) Vitamin D and Cancer. J. Cancer. Res. Ther., 3, 225–30.
Fletcher, J. E. (1980) On Facilitated Oxygen Diffusion in Muscle Tissues. Biophys. J., 29, 437–58.
Liguzinski, P. and Korzeniewski, B. (2006) Metabolic Control over the Oxygen Consumption Flux in Intact Skeletal Muscle: In Silico Studies. Am. J. Physiol. Cell Physiol., 291, C1213–24.
Mathews, J. H. and Fink, K. D. (2004) Numerical Methods Using Matlab (Upper Saddle River, NJ: Pearson Prentice Hall).
Scarborough, J. B. (1966) Numerical Mathematical Analysis (Baltimore, MD: The John Hopkins Press).
Tanenbaum, A. S. (1999) Structured Computer Organization (Upper Saddle River, NJ: Prentice Hall).
Wojciechowski, J. C., Narasipura, S. D., Charles, N., Mickelsen, D., Rana, K., Blair, M. L., and King, M. R. (2008) Capture and Enrichment of CD34-Positive Haematopoietic Stem and Progenitor Cells from Blood Circulation Using P-Selectin in an Implantable device. Br. J. Haematol., 140, 673–81.