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Description : Partial Differential Equations (PDE) are nowadays an essential mathematical object for the study and understanding of physical or biological phenomena. Their great complexity often makes them impossible to solve analytically; hence the need to use numerical solution methods.

This course is dedicated to the introduction of PDEs, then to their solution using well-known numerical schemes such as finite difference and finite volume methods. A more analytical part, necessary for the introduction of finite volume methods, will be devoted to the analytical resolution of scalar conservation laws. Four programming exercises will illustrate the scientific computing tools seen in the course with simple examples.

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The construction of solutions of partial differential equations (PDEs) and the theoretical study of their qualitative behavior is essentially based on the use of analytical results and in particular of functional analysis. This course presents the first important tools for the solution of PDEs via analytical or geometrical points of view. These tools will be implemented in the study of some examples of PDEs representative of large classes of equations.

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