Difference between revisions of "Scilab/C4/ODE-Applications/English-timed"

|Dear Friends, Welcome to the Spoken Tutorial on '''Solving ODEs using Scilab ode function'''  

| Use Scilab ode function

| Solve typical examples of '''ODEs''' and  

| Plot the solution.

|The typical examples will be:

| Motion of '''simple pendulum'''

| '''Van der Pol equation'''

| and ''' Lorenz system'''.

|and '''Scilab 5.3.3''' version.

|To practice this tutorial, a learner should have basic knowledge of '''Scilab'''  

|The '''ode''' function is an '''ordinary differential equation solver'''.

||The syntax is '''y equal to ode''' within parenthesis '''y zero, t zero, t''' and '''f'''.

|| Here '''y zero''' is the initial condition of the '''ODEs''',

| '''t zero''' is the '''initial time''',

|'''t''' is the '''time range''',  

|and '''f''' is the '''function'''.

|We are given the initial conditions-

|'''theta of zero''' is equal to '''pi by four''' and  

|''' l equal to zero point five meter''' is the length of the '''pendulum.'''  

|Open '''Pendulum dot sci''' on '''Scilab editor.'''  

|Then we call the '''ode''' function with arguments '''y zero, t zero, t''' and the function '''Pendulum.'''  

| The solution to the equation will be a '''matrix''' with two '''rows.'''  

|Save and execute the file '''Pendulum dot sci'''.

|Switch to '''Scilab console'''.

|Let us solve '''Van der Pol equation''' using the '''ode''' function.

|We are given the '''equation '''-

|The initial conditions are '''v of two equal to one''' and '''v dash of two equal to zero. '''

|We have to find the solution within the '''time range two less than t less than ten''' and then '''plot'''  the solution.  

| Switch to '''Scilab editor''' and open '''Vander pol dot sci.'''

| Then we define the '''function Vander pol''' and construct a system of '''first order ODEs.'''  

| Then we call '''ode''' function and solve the system of '''equations.'''  

| Save and execute the file '''Vander pol dot sci.'''  

|The '''Lorenz system of equations''' is given by:  

|'''x one dash equal to sigma into x two minus x one''',

|'''x two dash equal to one plus r minus x three into x one minus x two''' and

|The initial conditions are '''x one zero equal to minus ten''',  '''x two zero equal to ten''' and '''x three zero equal to twenty five.'''  

|Let '''sigma''' be equal to '''ten,  r''' be equal to '''twenty eight''' and '''b''' equal to '''eight by three.'''

|Switch to '''Scilab editor''' and open '''Lorenz dot sci'''.

|We define the '''function Lorenz''' and then define the given constants '''sigma, r''' and '''b.'''

|Then we define the '''first order ODEs.'''

|Then we call the '''ode''' function to solve the '''Lorenz system of equations.'''  

|Then we '''plot x one, x two''' and '''x three versus time.'''

|In this tutorial we have learnt to develop '''Scilab code''' to solve an '''ODE''' using '''Scilab ode function'''.

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| It summarizes the Spoken Tutorial project.

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