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Automatic derivative evaluation in solving boundary value problems: the renal medulla.

A S Wexler, R E Kalaba, D J Marsh

The American Journal of Physiology

|August 1, 1986

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This study introduces FORTRAN subroutines for automatic derivative evaluation, simplifying complex equation solving. This method successfully tackled a challenging 13th-order boundary-value problem in renal modeling.

Area of Science:

Numerical analysis
Computational mathematics
Biomedical modeling

Background:

Solving large systems of equations with many variables necessitates efficient derivative evaluation.
Existing numerical methods for complex models, such as those of the renal concentrating mechanism, can be computationally intensive.
Simulating intricate biological structures like the renal medulla requires advanced computational approaches.

Purpose of the Study:

To present a set of user-friendly FORTRAN subroutines for automatic derivative evaluation.
To demonstrate the application of these subroutines in solving a complex 13th-order boundary-value problem.
To highlight the potential of this approach for tackling larger, more complex simulations in biomedical research.

Main Methods:

Related Experiment Videos

Development and implementation of FORTRAN subroutines for automatic differentiation.

Application of the method of quasilinearization in conjunction with automatic differentiation.

Solving a 13th-order boundary-value problem relevant to renal concentrating mechanism models.

Main Results:

The developed subroutines provide an efficient means for automatic derivative evaluation.
The quasilinearization method, enhanced by automatic differentiation, yielded results consistent with finite difference and multiple shooting methods.
The approach proved effective for a challenging 13th-order boundary-value problem.

Conclusions:

Automatic derivative evaluation using the presented subroutines simplifies the solution of large systems of equations.
This method offers a practical advantage for solving complex boundary-value problems, particularly in the context of physiological modeling.
The approach is scalable and holds significant potential for simulating three-dimensional structures, such as the renal medulla.