Ordinary Differential Equations

John M. Neuberger ()
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John M. Neuberger: Northern Arizona University, Department of Mathematics and Statistics

Chapter Chapter 3 in Difference Matrices for ODE and PDE, 2023, pp 63-92 from Springer

Abstract: Summary In this chapter, we use difference matrices to solve ordinary differential equations. We first apply Newton’s method to a second-order elliptic semilinear boundary value problem. Next, we use MATLAB®’s built-in linear system solver ‘backslash’ to solve a linear ordinary second-order boundary value problem. An eigenvalue problem is solved using second difference matrices, and Fourier Sine series are used to introduce eigenfunction expansion. Next, we consider how to enforce 0-Dirichlet, 0-Neumann, and periodic boundary conditions using both point grid and cell grid. We solve first-order initial value problems, linear systems of first-order linear initial value problems, and first-order nonlinear initial value problems. The difference matrix approach is compared with more traditional ordinary differential equation solvers, e.g., Runge–Kutta and MATLAB’s built-in solver ode45.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-12000-8_3

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DOI: 10.1007/978-3-031-12000-8_3

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