Gear4

gear4(dydt, t_start, t_end, nstep, y0)

Input:

dydt is a user defined function of the form dydt(t, y) => {some expression of y and t}

t_start is a real number for initial time

t_end is a real number of end time

nstep is an positive integer implies the preferred time steps for the solutions

y0 is a real number for the initial value of y when t = t_start  

Result:

A row vector gives the time points of t for the solutions

A column vector gives the solutions y for the time points t.

gear4(dydt, t_start, t_end, nstep, y0, abserr, relerr)

Input:

dydt is a user defined function of the form dydt(y, t) => {some expression of y and t}

t_start is a real number for initial time

t_end is a real number of end time

nstep is an positive integer implies the preferred time steps for the solutions

y0 is a real number for the initial value of y when t = t_start  

abserr is a real number for absolute tolerance

relerr is a real number for relative tolerance

Result:

A row vector gives the time points of t for the solutions

A column vector gives the solutions y for the time points t.

gear4(dydt, t, y0)

Input:

dydt is a user defined function of the form dydt(y, t) => {some expression of y and t}

t is a row/column vector which gives the preferred time points for the solutions

y0 is a real number for the initial value of y when t = t[0]

Result:

A row vector gives the time points of t for the solutions

A column vector gives the solutions y for the time points t.

gear4(dydt, t, y0, abserr, relerr)

Input:

dydt is a user defined function of the form dydt(y, t) => {some expression of y and t}

t is a row/column vector which gives the preferred time points for the solutions

y0 is a real number for the initial value of y when t = t[0]

abserr is a real number for absolute tolerance

relerr is a real number for relative tolerance

Result:

A row vector gives the time points of t for the solutions

A column vector gives the solutions y for the time points t.

gear4(<dy1dt, ...>, t_start, t_end, nstep, y0)

Input:

<dy1dt, dy2dt, ...> is a group of user defined functions of the form dydt(t, y1, y2, ...) => {some expression of t, y1, y2, ...}, which are enclosed with '<>' . These functions defined the all 1st-order IVP differential equations converted from the high-order ODE.

t_start is a real number for initial time

t_end is a real number of end time

nstep is an positive integer implies the preferred time steps for the solutions

y0 is a real number for the initial value of y when t = t_start  

Result:

A row vector gives the time points of t for the solutions

A matrix gives the solutions y for the time points t whose first column is solution for y1, second row for y2, etc.

gear4(<dy1dt, ...>, t_start, t_end, nstep, y0, abserr, relerr)

Input:

<dy1dt, dy2dt, ...> is a group of user defined functions of the form dydt(t, y1, y2, ...) => {some expression of t, y1, y2, ...}, which are enclosed with '<>' . These functions defined the all 1st-order IVP differential equations converted from the high-order ODE.

t_start is a real number for initial time

t_end is a real number of end time

nstep is an positive integer implies the preferred time steps for the solutions

y0 is a real number for the initial value of y when t = t_start  

abserr is a real number for absolute tolerance

relerr is a real number for relative tolerance

Result:

A row vector gives the time points of t for the solutions

A matrix gives the solutions y for the time points t whose first column is solution for y1, second row for y2, etc.

gear4(<dy1dt, ...>, t, y0)

Input:

<dy1dt, dy2dt, ...> is a group of user defined functions of the form dydt(t, y1, y2, ...) => {some expression of t, y1, y2, ...}, which are enclosed with '<>' . These functions defined the all 1st-order IVP differential equations converted from the high-order ODE.

t is a row/column vector which gives the preferred time points for the solutions

y0 is a real number for the initial value of y when t = t[0]

Result:

A row vector gives the time points of t for the solutions

A matrix gives the solutions y for the time points t whose first column is solution for y1, second row for y2, etc.

gear4(<dy1dt, ...>, t, y0, abserr, relerr)

Input:

<dy1dt, dy2dt, ...> is a group of user defined functions of the form dydt(t, y1, y2, ...) => {some expression of t, y1, y2, ...}, which are enclosed with '<>' . These functions defined the all 1st-order IVP differential equations converted from the high-order ODE.

t is a row/column vector which gives the preferred time points for the solutions

y0 is a real number for the initial value of y when t = t[0]

abserr is a real number for absolute tolerance

relerr is a real number for relative tolerance

Result:

A row vector gives the time points of t for the solutions

A matrix gives the solutions y for the time points t whose first column is solution for y1, second row for y2, etc.

Input

Output

dy1dt(t, y1, y2) => y2

dy2dt(t, y1, y2) => -10000 * y1 + (-10001) * y2

gear4(<dy1dt, dy2dt>, 0, 20, 20, [1, -1])