W. E. Schiesser

Iacocca, D118

Lehigh University

111 Research Drive

Bethlehem, PA 18015 USA

(610) 758-4264 (office)

(610) 758-5057 (fax)

wes1@lehigh.edu

http://www.lehigh.edu/~wes1

http://eqworld.ipmnet.ru

Update 01AUG18

We are engaged in the development of algorithms and associated software
for the numerical integration of systems of ordinary differential
equations (ODEs),

differential algebraic equations (DAEs) and partial
differential equations (PDEs).

A summary of this development is in link.

Some selected references pertaining to this work are listed below:

Books:

(1) Schiesser, W. E. (1991), *The Numerical Method of Lines Integration
of Partial Differential Equations*, Academic Press, San Diego

(2) Silebi, C. A., and W. E. Schiesser (1992), *Dynamic Modeling of
Transport Process Systems*, Academic Press, San Diego

(3) Byrne, G. D., and W. E. Schiesser (eds.) (1992), *Recent Developments
in Numerical Methods and Software for ODEs/DAEs/PDEs*, World Scientific,
Singapore

(4) Schiesser, W. E. (1994), *Computational Mathematics in Engineering
and Applied Science: ODEs, DAEs, and PDEs*, CRC Press, Boca Raton

(5) Schiesser, W. E., and C. A. Silebi (1997), *Computational Transport
Phenomena*, Cambridge University Press, Cambridge, UK

(6) Vande Wouwer, A., Ph. Saucez and W. E. Schiesser (eds.) (2001),
*Adaptive Method of Lines*, CRC Press, Boca Raton

(7) Lee, H. J., and W. E. Schiesser (2004), *Ordinary and Partial
Differential Equation Routines in C, C++, Fortran, Java, Maple and Matlab*,CRC Press, Boca Raton

(8) Schiesser, W. E., and G. W. Griffiths (2009), *A Compendium of Partial
Differential Equations Models: Method of Lines Analysis with Matlab*,
Cambridge University Press, Cambridge, UK

(9) Griffiths, G. W., and W. E. Schiesser (2012), *Traveling Wave Analysis of Partial Differential
Equations: Numerical and Analytical Solutions with Matlab and Maple*, Academic Press/Elsevier,
Burlington, MA

(10) Schiesser, W. E. (2013), *Partial Differential Equation Analysis in Biomedical
Engineering*, Cambridge University Press, Cambridge, UK

(11) Schiesser, W. E. (2014), *Differential Equation Analysis in Biomedical Science and
Engineering, Ordinary Differential Equation Analysis with R*, John Wiley and Sons,
Hoboken, NJ

(12) Schiesser, W. E. (2014), *Differential Equation Analysis in Biomedical Science and
Engineering, Partial Differential Equation Analysis with R*, John Wiley and Sons,
Hoboken, NJ

(13) McHugh, A. J., G. W. Griffiths and W. E. Schiesser (2015), *An Introductory Global
CO2 Model*, World Scientific, Singapore

(14) Schiesser, W. E. (2016), *Method of Lines PDE Analysis in Biomedical Science and
Engineering*, John Wiley and Sons, Hoboken, NJ

(15) Schiesser, W.E. (2017), *Spline Collocation Analysis of Partial Differential
Equations*, John Wiley and Sons, Hoboken, NJ

(16) Schiesser, W.E. (2017), *Computational Chemotaxis Models for Neurodegenerative
Disease*, World Scientific, Singapore

(17) Schiesser, W.E. (2017), *Method of Lines Analysis of Turing Models*,
World Scientific, Singapore

(18) Schiesser, W.E. (2018), *ODE/PDE Alpha-synuclein Models for Parkinson's
Disease*, Academic Press/Elsevier, Cambridge, MA

(19) Salehi. Y., and W.E. Schiesser (2018), *Vol 1: Introduction to Algorithms and
Computer Coding in R *, Morgan and Claypool, San Rafael, CA

(20) Salehi, Y., and W.E. Schiesser (2018), *Vol 2: Applications from Classical
Integer PDEs *, Morgan and Claypool, San Rafael, CA

(21) Schiesser, W.E. (2019), *A Mathematical Modeling Approach to Infectious Diseases:
Cross Diffusion PDE Models for Epidemiology *, World Scientific, Singapore

(22) Schiesser, W.E. (2019), *Numerical PDE Analysis of the Blood Brain Barrier:
Method of Lines in R *, World Scientific, Singapore

The programs in references (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13) and (14) are available on request (the details for accessing these routines are given in this link).

The programs in references (15), (16), (17), (18), (19), (20), (21) and (22) are available from the publishers' Websites.

Selected book covers can be viewed through link.

Papers:

(1) Schiesser, W. E. (1996), *PDE Boundary Conditions from Minimum
Reduction of the PDE*, Applied Numerical Mathematics, v20, pp 171-179

(2) Saucez, P., A. Vande Wouwer and W. E. Schiesser (1996), *Some
Observations on a Static Remeshing Method Based on Equidistribution
Principles*, J. Computational Physics, v128, pp 274-288

(3) Lee. S. L., and W. E. Schiesser (1997), *Some Fundamental Limitations
of Mathematical Software Revealed by the Calculation of Spacetime
Curvature*, in Quality of Numerical Software, R. F. Boisvert (ed.),
pp 345-348, Chapman and Hall, London

(4) Taha, T. R., and W. E. Schiesser (1997), *Method of Lines Solution
of the K(2,2) (KdV-type) Equation*, Proceedings of the 15th IMACS World
Congress 1997, v2, Numerical Mathematics, pp 127-130, Berlin

(5) Vande Wouwer, A., P. Saucez and W. E. Schiesser (1998), *Some
User-oriented Comparisons of Adaptive Grid Methods for Partial Differential
Equations in One Space Dimension*, Applied Numerical Mathematics, v26,
pp 49-62

(6) Saucez, P., A. Vande Wouwer and W. E. Schiesser (1998), *An
Adaptive Method of Lines Solution of the Korteweg-de Vries Equation*,
Computers Math. Applic., v35, no. 12, pp 13-25

(7) Bloss, K. F., L. T. Biegler and W. E. Schiesser (1999), *
Dynamic Process Optimization through Adjoint Formulations and
Constraint Aggregation*, Ind. Eng. Chem. Res., v38, no. 2, pp 412-432

(8) Schiesser, W. E. (1999), * 'Computing in Physics' Prompts Model
Debate *, Physics Today, v52, no. 12, p 15,79

(9) Grandpierre, A. G., D. N. Christodoulides, W. E. Schiesser, C. M.
McIntosh and J. Toulouse (2001), *SRS Crosstalk in Massive WDM Systems
Under the Action of Group Velocity Dispersion*, Optics Communications,
6 JUNE 2001, pp 1-5

(10) Grandpierre, A. G., D. N. Christodoulides, W. E. Schiesser, C. M.
McIntosh and J. Toulouse (2001), *Stimulated Raman Scattering Crosstalk
in Massive WDM Systems Under the Action of Group Velocity Dispersion*,
Optics Communications, 15 JULY 2001, pp 319-323

(11) Saucez, Ph., W. E. Schiesser and A. Vande Wouwer (2001), *
Upwinding in the Method of Lines*, Mathematics and Computers
in Simulation, v56, no. 2, pp 171-185

(12) Hamdi, S., W. H. Enright, W. E. Schiesser and J. J. Gottlieb (2003),
*Exact Solutions of the Generalized Equal Width Wave Equations*,
Proceedings of the International Conference on Computational Science
and Its Applications - 2003, Springer-Verlag, LNCS 2668, Berlin,
pp 725-734

(13) Vande Wouwer, A., P. Saucez and W. E. Schiesser (2003),
*Numerical Experiments with the Moving Finite Element Method*,
Int. J. Pure and Applied Math., v4, no. 1, pp 1-31

(14) Hamdi, S., W. H. Enright, W. E. Schiesser and J. J. Gottlieb (2004),
*Exact Solutions and Invariants of Motion for General Types of Regularized
Long Wave Equations*, Journal of Mathematics and Computers in Simulation,
v65, no. 4/5, pp 535-545

(15) Vande Wouwer, A., P. Saucez and W. E. Schiesser (2004), *Simulation
of Distributed Parameter Systems Using a Matlab-Based Method of Lines
Toolbox: Chemical Engineering Applications*, Industrial and
Engineering Chemistry Research, v43, no. 14, pp 3469-3477

(16) Hamdi, S., W. H. Enright, Y. Ouellet and W. E. Schiesser (2004),
*Exact Solutions of Extended Boussinesq Equations*, Journal of
Numerical Algorithms v37, pp 165-175

(17) Griffiths, G. W., Ph. Saucez, A. Vande Wouwer and W. E. Schiesser
(2004), *Can a Nonlinearity be Neglected? An Example*, Mathematical
and Computer Modeling, v40, no. 11/12, pp 1393-1403

(18) Montesinos, R. M., A. Tejeda-Mansir, R. Guzman, J. Ortega and
W. E. Schiesser (2005), *Analysis and Simulation of Frontal Affinity
Chromatography of Proteins*, Separation Purification Technology,
v52, pp 75-84

(19) Hamdi, S., W. H. Enright, Y. Ouellet and W. E. Schiesser (2005),
*Method of Lines Solutions of the Extended Boussinesq Equations*,
Journal of Computational and Applied Mathematics, v183, no. 2, pp 327-342

(20) vande Wouwer, A., P. Saucez, W. E. Schiesser and S. Thompson (2005),
* A MATLAB Implementation of Upwind Finite Differences and Adaptive Grids
in the Method of Lines*, Journal of Computational and Applied Mathematics,
v183, no. 2, pp 245-258

(21) Hamdi, S., W. H. Enright, W. E. Schiesser and J. J. Gottlieb (2005),
*Exact Solutions and Conservation Laws for Coupled Generalized
Korteweg-de Vries and Quintic Regularized Long Wave Equations*,
Nonlinear Analysis, v63, pp e1425-e1434

(22) Calvert, P. D., K. J. Strissel, W. E. Schiesser, E. N. Pugh, Jr.,
and V. Y. Arshavsky (2006), *Light-driven Translocation of Signaling Proteins in
Vertebrate Photoreceptors*, Trends in Cell Biology, v16, pp 560-568

(23) Calvert, P. D., J. A. Peet, A. Bragin, W. E. Schiesser, and E. N. Pugh, Jr.
(2007), *Fluorescence Relaxation in 3D from Diffraction-limited Sources of PAGFP or
Sinks of EGFP Created by Multiphoton Photoconversion*, J. Microscopy and
Imaging, v225, pp 49-71

(24) Hamdi, S., W. E. Schiesser and G. W. Griffiths (2007), *The Method of Lines*,
on-line at Method of Lines,
2(7):2859

(25) Polyanin, A. D., W. E. Schiesser and A. I. Zhurov (2008), *Partial Differential Equation*,
on-line at Partial Differential
Equation, 3(10):4605

(26) Griffiths, G. W., and W. E. Schiesser (2009), *Linear and Nonlinear Waves*, on-line at
Linear and Nonlinear Waves,
4(7):4308

(27) Calvert, P. D., W. E. Schiesser, and E. N. Pugh, Jr. (2010), *Diffusion of a soluble protein,
photoactivatable GFP, through a sensory cilium*, J. General Physiology, v135(3), pp 173-196, s1-s8

(28) Cheng, H., H. S. Caram, W. E. Schiesser, J. M. Rickman, H. M. Chan and M. P. Harmer (2010),
*Oxygen grain-boundary transport in polycrystalline alumina using wedge-geometry bilayer samples:
Effect of Y-doping*, Acta Materialia, v59, pp 2442-2451

(29) Hamdi, S., B. Morse, B. Halphen, and W. E. Schiesser (2011), *Analytical solution of long, nonlinear
internal waves, Part I*, Nat. Hazards, v57, pp 597-607

(30) Hamdi, S., B. Morse, B. Halphen, and W. E. Schiesser (2011), *Analytical solution of long, nonlinear
internal waves, Part II*, Nat. Hazards, v57, pp 609-616

(31) Northrop, P. W. C., P. A. Ramachandran, W. E. Schiesser and V. R. Subramanian (2013), *Robust false
transient method of lines for elliptic partial differential equations*, Chem. Engr. Sci, v90, pp 32-39

(32) Gokhan, F. S., G. W. Griffiths and W. E. Schiesser (2013), *Method of lines solution to the
transient SBS equations for nanosecond Stokes pulses*, J. Europ. Opt. Soc. Rap. Public., v8,
pp 13049, 1-11

(33) Plociniczak, L., G. W. Griffiths and W. E. Schiesser (2014), *ODE/PDE analysis of corneal
curvature*, Computers in Biology and Medicine, v53, pp 30-41

(34) Gokhan, F. S., G. W. Griffiths and W. E. Schiesser (2014), *Method of lines solutions for
the three-wave model of Brillouin equations*, Engr. Comp.: Int. J. Computer-aided Engr. and Soft.,
v31(3), pp 388-405

(35) Linares, O. A., W. E. Schiesser, J. Fudin, T. C. Pham, J. J. Bettinger, R. O. Mathew and A. L. Daly
(2015), *In silico ordinary differential equation/partial differential equation hemodialysis model
estimates methadone removal during dialysis*, J. Pain Research, v8, pp 417–429

(36) Griffiths, G. W., L. Plociniczak, and W. E. Schiesser (2016), *Analysis of cornea
curvature using radial basis functions – Part I: Methodology *, Computers in Biology and Medicine,
v77, pp 274-284

(37) Griffiths, G. W., L. Plociniczak, and W. E. Schiesser (2016), *Analysis of cornea
curvature using radial basis functions – Part II: Fitting to data-set*, Computers in Biology and Medicine,
v77, pp 285-296

(38) Xu, N., Y. Ding, W. E. Schiesser, and M. V. Kothare (2016), *Mathematical
simulation of wet spinning coagulation process: Dynamic modeling and numerical results*, AIChE Journal, v62,
no. 9, September 2016, pp 3432–3440

(39) Kamel, Al-K., N. Haynes, W. E. Schiesser and M. Usman (2018), *Eventual periodicity of the
forced oscillations for a Korteweg–de Vries type equation on a bounded domain using a sinc collocation
method*, Journal of Computational and Applied Mathematics, v330, pp 417-428

(40) Salehi, Y., M. T. Darvishi, and W. E. Schiesser (2018), *Numerical solution of
space fractional diffusion equation by the method of lines and splines*, Applied Mathematics and
Computation, v336, pp 465-480

An introduction to the method of lines (MOL) solution of partial differential equations is available in link.

A partial list of the applications of our ODE/DAE/PDE software appears in link.

A partial list of organizations requesting our ODE/DAE/PDE software in 2007-2018 is available from link.

For maps to Lehigh, maps.

To contact me, send e-mail to wes1@lehigh.edu. To return to Lehigh's home page, click here.