Solving linear boundary value problems for linear systems of ordinary differential equations

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Rodríguez Molina, Marcos Javier
Embargoed Until
Shramchenko, Alexander
College of Arts and Sciences - Art
Department of Mathematics
Degree Level
This research studies the behavior of a numerical technique, known as Continuous Orthonormalization (CO), when computing the eigenfunction for the Orr-Sommerfeld equation (OSE). The hydrodynamic stability region of moving fluids, which are constrained to parallel flows, is of relevance and the OSE allows its understanding. CO pursues the generation of an orthogonal vector space constituted by the individual solutions of OSE. By doing this, major numerical errors influencing the computed solution are avoided. Noteworthy is the intrinsic flexibility of CO which allows its use in computing the solution of ordinary linear differential equations of diverse complexity. An important characteristic of CO is the use of numerical strategies of great reliability which are not normally applied to problems.such as OSE.

Esta investigación estudia el comportamiento de una técnica numérica, conocida como Ortonormalización Continua (OC), al computar la autofunción para la ecuación de Orr-Sommerfeld (EOS). La región de estabilidad hidrodinámica de fluidos en movimiento, restringido a flujo paralelo, es de relevancia y la EOS permite su entendimiento. OC persigue generar un espacio vectorial ortogonal constituido por las soluciones individuales de EOS. Al hacer esto, se evitan los grandes errores numéricos que influyen al cómputo de la solución. Notable es la flexibilidad intrínseca de OC que permite su uso al evaluar la solución de ecuaciones diferenciales ordinarias de variada complejidad. Una importante característica de OC es el uso de estrategias numéricas de gran confiabilidad que normalmente no son aplicadas a problemas como EOS.
Orthogonal vector space,
Wolfram language,
Moore-Penrose pseudoinverse
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Rodríguez Molina, M. J. (2019). Solving linear boundary value problems for linear systems of ordinary differential equations [Thesis]. Retrieved from