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2019

Civil Engineering Graduate Theses & Dissertations

Partial Differential Equations

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Strong Form Meshfree Collocation Method For Higher Order And Nonlinear Pdes In Engineering Applications, Andrew Christian Beel Jan 2019

Strong Form Meshfree Collocation Method For Higher Order And Nonlinear Pdes In Engineering Applications, Andrew Christian Beel

Civil Engineering Graduate Theses & Dissertations

The strong form meshfree collocation method based on Taylor approximation and moving least squares is an alternative to finite element methods for solving partial differential equations in engineering applications. This study examines how the proposed alternative method solves (i) higher-order and (ii) nonlinear partial differential equations. First, the proposed method is formulated in Chapter 2 for the general discretization and solution of strong forms of partial differential equations. Chapter 3 presents the convergence and error behavior of the proposed method for the fourth-order Stommel-Munk equation for wind-driven ocean circulation, as well as the numerical solution of this equation on a ...