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Practical Scientific Computing by V Zalizniak, A Muhammad

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10

Introduction to Finite Difference Schemes for Ordinary Differential Equations

Consideration of problems in the natural sciences and engineering often leads to differential equations, and the study of such problems requires solving these equations. In some cases, it is possible to write their solutions in terms of known elementary functions. As a rule, however, this in principle is impossible, so that the construction of a solution in terms of an explicit closed-form expression cannot be considered as a standard method for solving differential equations. One cannot say that the analytic approach has lost its value. It remains a necessary instrument for the study of simplified, so called model problems. The study of model problems allows one ...

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