All Outputs (13)

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.

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..

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..

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 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 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.

Series solutions of partial differential equations using the complex integral method (2014)
Journal Article
Robin, W. (2014). Series solutions of partial differential equations using the complex integral method. International Mathematical Forum, 9, 1477-1494. https://doi.org/10.12988/imf.2014.48145

The complex integral method for solving ordinary differential equations in series [3, 7, 8] is extended to cover the series solution of partial differential equations also. The means of this extension is straightforward, with both ‘ordinary’ and ‘Fro... Read More about Series solutions of partial differential equations using the complex integral method.

Similarity solutions to unsteady pseudoplastic flow near a moving wall (2014)
Journal Article
Robin, W. (2014). Similarity solutions to unsteady pseudoplastic flow near a moving wall. International Mathematical Forum, 9(31), 1465-1475. https://doi.org/10.12988/imf.2014.418

It is shown that similarity solutions to a partial differential boundary value problem for power law fluids may be generated by the application of a multi-parameter stretching group. Furthermore, the resulting ordinary differential boundary value... Read More about Similarity solutions to unsteady pseudoplastic flow near a moving wall.

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.

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.