The aim of this course is to present an overview of high-order accurate numerical methods for mathematical problems that arise in aeronautical and aerospace engineering. Numerical schemes are referred to as high-order accurate when a suitably defined error measure e is a function of the mesh size h as e∼h^p, with p≥3. High-order accuracy is of significant engineering interest in numerical methods because it allows the solution of computational problems with a smaller number of degrees of freedom and higher convergence rates of the error with respect to low-order numerical schemes. The aim of this course is to present an overview of high-order accurate numerical methods for mathematical problems that arise in aeronautical and aerospace engineering. Numerical schemes are referred to as high-order accurate when a suitably defined error measure e is a function of the mesh size h as e∼h^p, with p≥3. High-order accuracy is of significant engineering interest in numerical methods because it allows the solution of computational problems with a smaller number of degrees of freedom and higher convergence rates of the error with respect to low-order numerical schemes.

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