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Analyzing Runga-Kutta Methods for Solving Initial Value Problems in ODEs

This work explores the Runga-Kutta methods as a numerical approach to solve initial value problems in ordinary differential equations (ODEs). Unlike Taylor methods, which can be complicated and time-consuming, Runga-Kutta methods offer a more efficient and reliable alternative. We discuss the implications of error propagation, particularly in relation to the Euler method's predictions, and highlight how increasing the variable x can escalate the error. The paper aims to provide insights into the practicality and application of these methods in solving ODEs.

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Analyzing Runga-Kutta Methods for Solving Initial Value Problems in ODEs

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    1. Rung_Kutta Methods

    2. Initial_Value Problems for Ordinary Differential Equation(ODE) ,

    3. we know

    4. So

    5.   taylor methods is a complicated and time_consuming procedure for most problems so, taylor methods are seldom used.

    6. i=0

    7. Az consider above Euler method predicts point B inested of point A, therefore we except by increasing the variable x the value of error will be increased

    11. `

    12. Refrence :

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