Find 2 equations of first order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using the second  order Runge Kutta method to find  the first 3 points of the solution domain. Compare the solution of  second order Runge Kutta method to second order Taylor method. Give comments based on the comparison of both methods in terms of absolute error and computational cost / time.  Draw the graft of solution  and develop the table of the calculation process.

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Find a first order ODE problem to present the physical problem with initial condition with h size of interval.  Choose single step method and solve these IVP of ODE above. Compare the solution of single step method to multistep method. Describe the concept of explicit and implicit schemes of the both methods. Give comments based on the comparison of both methods in terms of absolute error and computational cost.  Draw the graft of  solution  and develop the table of the calculation process.

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Find 3 equations of first order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using the second  order Runge Kutta method to find  the first 2 points of the solution domain. Compare the solution of  second order Runge Kutta method to the Euler method. Give comments based on the comparison of both methods in terms of absolute error and computational cost / time.  Draw the graft of solution  and develop the table of the calculation process.

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Find a second order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using the third order Taylor method to find  the first 3 points of the solution domain. Compare the solution of  the third order Taylor method to Euler method. Give comment based on the comparison of both methods in terms of absolute error and computational cost / time. Draw the graft of solution  and develop the table of the calculation process.

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Find a first order ODE problem to present the physical problem with initial condition with h size of interval.  Choose single step method and solve these IVP of ODE above. Compare the solution of single step method to multistep method. Describe the concept of explicit and implicit schemes of the both methods. Give comments based on the comparison of both methods in terms of absolute error and computational cost.  Draw the graft of  solution  and develop the table of the calculation process.

How Geogebra helps  to validate your solution above? Can you show it?

Find a third order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using a second order Taylor method to find  the first 2 points of the solution domain. Compare the solution of  second order Taylor method to Euler method. Give comment based on the comparison of both methods in terms of absolute error and computational cost / time. Draw the graft of  solution  and develop the table of the calculation process.

How Geogebra helps  to validate your solution above? Can you show it?

Find 3 equations of first order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using the second  order Runge Kutta method to find  the first 2 points of the solution domain. Compare the solution of  second order Runge Kutta method to the Euler method. Give comments based on the comparison of both methods in terms of absolute error and computational cost / time.  Draw the graft of solution  and develop the table of the calculation process.

How Geogebra helps  to validate your solution above? Can you show it?

Project 5

Find a first order ODE problem to present the physical problem with initial condition with h size of interval and find initial solutions using Euler method. These initial solutions will use to obtain the first 3 points of the solution domain  using 3 steps predictor  method. Correct the solution of predictor method using  3 steps corrector method. Control the iteration of corrector method with convergent criterion. Give comments based on the comparison of both methods in terms of absolute error and computational cost between predictor and corrector method.  Draw the graft of  solution  and develop the table of the calculation process.

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Find a third order ODE problem to present the physical problem with initial condition with h size of interval. Solve the problem using a second order Taylor method to find  the first 2 points of the solution domain. Compare the solution of  second order Taylor method to Euler method. Give comment based on the comparison of both methods in terms of absolute error and computational cost / time. Draw the graft of  solution  and develop the table of the calculation process.

How Geogebra helps  to validate your solution above? Can you show it?