Iterative solutions to classical second-order ordinary differential equations (2019)
Journal Article
Robin, W. (2019). Iterative solutions to classical second-order ordinary differential equations. Journal of Innovative Technology and Education, 6(1), 1-12

An elementary scheme is detailed for introducing certain basic concepts in the solution of (especially) the basic second-order ordinary differential equations of classical mathematical physics. The method proposed, an integration/iteration process, a... Read More about Iterative solutions to classical second-order ordinary differential equations.

Some new uniform approximate analytical representations of the Blasius function. (2015)
Journal Article
Robin, W. (2015). Some new uniform approximate analytical representations of the Blasius function. Global Journal of Mathematics, 2, 150-155

New uniform approximations of the Blasius velocity profile and Blasius function are developed from existing rational approximations of the Blasius velocity profile and of the Blasius function itself. Essentially, the existing rational approximations... Read More about Some new uniform approximate analytical representations of the Blasius function..

On compact uniform analytical approximations to the Blasius Velocity profile. (2015)
Journal Article
Robin, W. (2015). On compact uniform analytical approximations to the Blasius Velocity profile. International Mathematical Forum, 10, 311-322. https://doi.org/10.12988/imf.2015.514

It is shown that approximate analytical representations of the Blasius function may be developed by using the error function, erf (ax), for positive constant a, as a basic compact approximate form for the derivative of the Blasius function, that is,... Read More about On compact uniform analytical approximations to the Blasius Velocity profile..

Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 953-965. https://doi.org/10.12988/imf.2014.4491

A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of fin... Read More about Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration.

Ladder-Operator Factorization and the Bessel Differential Equations (2014)
Journal Article
Robin, W. (2014). Ladder-Operator Factorization and the Bessel Differential Equations. International Mathematical Forum, 9, 71-80. https://doi.org/10.12988/imf.2014.311214

We present an alternative approach to the discussion of Bessel equations and Bessel functions, through an elementary factorization method. The various Bessel equations are represented by a single parameterized form and, after a standard transformatio... Read More about Ladder-Operator Factorization and the Bessel Differential Equations.

On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. Nonlinear Analysis and Differential Equations, 2, 155-171. https://doi.org/10.12988/nade.2014.4712

The theory of series solutions for two important classes of the general higher-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression derived and applied in previous papers [10,... Read More about On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method..

Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 967-976. https://doi.org/10.12988/imf.2014.4492

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the meth... Read More about Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration.

On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method. Nonlinear Analysis and Differential Equations, 2(4), 173-188. https://doi.org/10.12988/nade.2014.4713

The theory of series solutions for second-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression (based on Herrera’ work [3]) derived and applied in previous papers [8, 9]. As w... Read More about On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method.

On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation (2013)
Journal Article
Robin, W. (2013). On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation. International Mathematical Forum, 8, 1455-1466. https://doi.org/10.12988/imf.2013.37133

In this paper, we present a new systematic approach to the solution of the hypergeometric-like differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of... Read More about On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation.

Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation (2013)
Journal Article
Robin, W. (2013). Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation. International Mathematical Forum, 8, 1205-1213. https://doi.org/10.12988/imf.2013.3478

We present an new angle on the introduction of the homotopy-analysis method of Liao [6]. The homotopy-analysis method is then applied to produce a series solution of the Blasius problem in two different ways and comparison made with the work of Wang... Read More about Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation.

The Scottish Mathematics Support Network (2012)
Journal Article
Ahmed, S., & Durkacz, K. (2012). The Scottish Mathematics Support Network. MSOR Connections, 12, 42-44. https://doi.org/10.11120/msor.2012.12020042

The preliminary meeting of the Scottish Mathematics Support Network was held at the University of St Andrews on 18 July 2008. The aim of the meeting was to initialise a support network for people working in Scottish Universities and Colleges who were... Read More about The Scottish Mathematics Support Network.

On the Rodrigues’ Formula Approach to Operator Factorization (2012)
Journal Article
Robin, W. (2012). On the Rodrigues’ Formula Approach to Operator Factorization. International Mathematical Forum, 7(45-48), 2333-2351

In this paper, we derive general formulae that reproduce well-known instances of recurrence relations for the classical orthogonal polynomials as special cases. These recurrence relations are derived, using only elementary mathematics, directly from... Read More about On the Rodrigues’ Formula Approach to Operator Factorization.

The 4th Scottish Maths Support Network meeting 2011 (2012)
Journal Article
Ahmed, S., Barnes, S., & Durkacz, K. (2012). The 4th Scottish Maths Support Network meeting 2011. MSOR Connections, 12, 43-45. https://doi.org/10.11120/msor.2012.12010043

This year the annual meeting of the Scottish Maths Support network (SMSN) was held at the University of Strathclyde on Friday 9 September. Almost all Scottish universities were represented along with one attendee from Ireland. The meeting was organis... Read More about The 4th Scottish Maths Support Network meeting 2011.

Evaluation of the accuracy of mathematical models through use of multiple metrics. (2011)
Journal Article
Caliskan, N., Jadraque, E., Tham, Y. W., & Muneer, T. (2011). Evaluation of the accuracy of mathematical models through use of multiple metrics. Sustainable Cities and Society SCC, 1, 63-66. https://doi.org/10.1016/j.scs.2011.02.001

Engineering practise heavily relies on the development and use of mathematical models. In this article a number of appropriate metrics have been selected to provide an insight in the validation of models and also to obtain a figure of merit for any g... Read More about Evaluation of the accuracy of mathematical models through use of multiple metrics..

Modeling Pedestrian Walking Speeds on Sidewalks (2007)
Journal Article
Raeside, R., & Al-Azzawi, M. (2007). Modeling Pedestrian Walking Speeds on Sidewalks. Journal of Urban Planning and Development, 133(3), 211-219. https://doi.org/10.1061/%28ASCE%290733-9488%282007%29133%3A3%28211%29

Several models have been created over the years that are used in simulation packages to predict pedestrian speed and flow on sidewalks. However, the predictive power of these models has been weak. In this paper the results of a modeling exercise in t... Read More about Modeling Pedestrian Walking Speeds on Sidewalks.

Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration. (2007)
Journal Article
Wood, J., Muneer, T., & Kubie, J. (2007). Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration. Journal of Solar Energy Engineering, 125, 1-6. https://doi.org/10.1115/1.1531149

A new integrated device (called the BF3) has been developed, which enables the simultaneous measurement of horizontal global and diffuse irradiance as well as sunshine presence at any time. The sensor needs no specific polar alignment or routine adju... Read More about Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration..

Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function (2006)
Journal Article
Zhang, H., & Kuang, J. S. (2007). Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function. International Journal for Numerical Methods in Engineering, 69(7), 1345-1373. https://doi.org/10.1002/nme.1809

A new eight-node Reissner-Mindlin plate element is developed with a special interpolation within the element. This special interpolation is an extension of the element boundary interpolation that employs Timoshenko beam function for the boundary segm... Read More about Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function.

Integrating Information About Complex Systems: Role of Metadata in the Acceptability of Results from Models (2006)
Journal Article
Westlake, A., & Wigan, M. (2006). Integrating Information About Complex Systems: Role of Metadata in the Acceptability of Results from Models. Transportation research record, 1972, 60-68. https://doi.org/10.3141/1972-10

Opus is a project funded by the European Union Statistical Agency (Eurostat). The project is developing a methodology for the coherent and consistent integration of information from multiple sources about complex systems (based on Bayesian statistica... Read More about Integrating Information About Complex Systems: Role of Metadata in the Acceptability of Results from Models.

Stochastic social optimum traffic assignment (2005)
Journal Article
Maher, M., Stewart, K., & Rosa, A. (2005). Stochastic social optimum traffic assignment. Transportation Research Part B: Methodological, 39(8), 753-767. https://doi.org/10.1016/j.trb.2004.10.001

This paper formulates a Stochastic Social Optimum (SSO) that relates to the Stochastic User Equilibrium (SUE) in the same way as the Social Optimum (SO) relates to the User Equilibrium (UE) in a deterministic environment. At the SSO solution, the tot... Read More about Stochastic social optimum traffic assignment.

Wavelet analysis of the ECG: A review (2005)
Journal Article
Addison, P. (2005). Wavelet analysis of the ECG: A review. Physiological Measurement, 26(5), 155-199. https://doi.org/10.1088/0967-3334/26/5/R01

The wavelet transform has emerged over recent years as a powerful time–frequency analysis and signal coding tool favoured for the interrogation of complex nonstationary signals. Its application to biosignal processing has been at the forefront of the... Read More about Wavelet analysis of the ECG: A review.