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This chapter extends the numerical methods and software tools from Chapters 1–3 to nonlinear partial differential equations. Chapter 4.1 deals with discretization techniques for nonlinear terms in PDEs and algorithms for solving systems of nonlinear algebraic equations, whereas software tools supporting the implementation of the methods in Chapter 4.1 are described in Chapter 4.2. The application areas are limited to scalar PDEs, but the methodology in this chapter is applied to systems of PDEs and more challenging applications in Chapters 5.2, 6.3, and 7.
KeywordsNonlinear Problem Model Problem Continuation Method Nonlinear Algebraic Equation Finite Element Discretization
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