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Applied Mathematical Methods by Bhaskar Dasgupta

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ODE Solutions: Advanced Issues

In the previous chapter, we had a bird’s-eye view on the basic numerical methods for solving ODE systems as initial value problems. In this chapter, we consider special issues. First, we examine the methods of solving IVP’s for their stability and discuss their revision for stiff differential equations. Then, we also discuss numerical methods to solve boundary value problems in ODE’s.

Stability Analysis

With adaptive step size, the fourth order Runge-Kutta method is so successful in solving applied problems that many students and researchers in applied sciences take it for granted, till the day their favourite RK4 calls a strike. A docile labourer like RK4 does call a strike, when it is called to solve a stiff ...

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