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first, second or third year university students who are specializing in math- ematics or a ... are elementary methods for solving them, and modern computers make it ... assigned to crack a secret cipher constructed as follows. ... Exercise 7.31.. In solving PDEs numerically, the following are essential to consider: • physical ... ical understanding),. • stability/accuracy analysis of numerical methods (math- ... re-meshing, for ex- ample, in crack propagation problems and large de- ... It suffices to consider the algebraic equations of (7.31) at interface grid .... Discrete fracture and damage tools were utilized to model crack initiation and propagation in pavement systems using the finite ... Table 7.31. Direct Tension ... calculate the thermal stresses, assuming either a pseudo-elastic slab or beam and solving ... A system of non-linear algebraic equations was obtained based on the.. situations. We derive the basic equations of linear elasticity by reference to the ... 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