The purpose of this thesis is to study pseudospectral methods and to implement the algorithm that solves two point boundary value problems by pseudospectral methods. Another purpose of this thesis is to implement that algorithm into an application for solving two point boundary value problems. The rst part of the thesis presents theoretical concepts needed to understand the pseudospectral methods such as: di�erential equations, boundary value problems and few more. This is followed by the theoretical idea of pseudospectral methods and algorithm in theory. The last part consists of practical implementation and explanation of how application works followed by few examples.
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