Titlebook: Difference Matrices for ODE and PDE; A MATLAB? Companion John M. Neuberger Textbook 2023 Springer Nature Switzerland AG 2023 difference mat

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J. Hill,H. C. Becker,P. M. A. Tigerstedtary conditions to extend the ideas developed in Chap.?. to partial differential equations. In particular, for the square domain we investigate eigenvalues of the Laplacian, solutions to semilinear elliptic boundary value problems, Laplace’s equation with nonhomogeneous boundary conditions, the heat

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J. Hill,H. C. Becker,P. M. A. Tigerstedtof semilinear elliptic BVP. The tangent Newton method is used for branch following. The secant method is used for bifurcation detection. The mountain pass and modified mountain pass algorithms are used for finding the Morse index one and two solutions. We also compute solutions for fully nonlinear e

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Introduction,mphasize the usefulness of the MATLAB debugger. We discuss the process of converting code fragments and hints from the text into working programs, and give some suggestions to instructors on the assignment of the homework problems which require those working programs. We give more detail concerning each of the specific included topics.

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Advanced Topics in Semilinear Elliptic BVP,of semilinear elliptic BVP. The tangent Newton method is used for branch following. The secant method is used for bifurcation detection. The mountain pass and modified mountain pass algorithms are used for finding the Morse index one and two solutions. We also compute solutions for fully nonlinear equations involving the .-Laplacian.

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