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Applied Mathematical Methods by Bhaskar Dasgupta

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29

Numerical Solution of Ordinary Differential Equations

The natural step after the study of numerical quadrature is that of numerical solution of ordinary differential equations (ODE’s). As the reader is aware, ordinary differential equations turn up as mathematical models in almost all fields of quantitative analysis. Leaving a few fortunate situations, one has to depend upon numerical analysis for the solution.1

In this chapter, we refresh the background of basic methods of numerical solution of single first order ODE’s and establish the methodology for applying them to problems of ODE systems. Why and under what conditions such solutions make sense are questions that are deferred to Chap. 31.

Single-Step Methods

It is assumed here that the ...

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