Below is my code for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

Define RR to be the real numbers, rounding to the nearest number, with 25 bits of precision

RR = RealField(25,rnd='RNDN')

Define t,x,y to be numbers in RR

t,x,y = PolynomialRing(RR,3,"txy").gens()

Define the system of equations

firsteq = y secondeq = -x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

Define parameters

t0 = 0 x0 = 0 y0 = 2 h = 1/4 n = 10 t1 = t0 + n*h

Plot the x(t) and y(t) graphs

eulers_method_2x2_plot(firsteq , secondeq, t0, x0, y0, h, t1)

Below is my code step bby step for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

Define RR to be the real numbers, rounding to the nearest number, with 25 bits of precision

RR = RealField(25,rnd='RNDN')

Define t,x,y to be numbers in RR

t,x,y = PolynomialRing(RR,3,"txy").gens()

Define the system of equations

firsteq = y y

secondeq = -x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

Define parameters

t0 = 0 0

x0 = 0 0

y0 = 2 2

h = 1/4 1/4

n = 10 10

t1 = t0 + n*h

Plot the x(t) and y(t) graphs

eulers_method_2x2_plot(firsteq , secondeq, t0, x0, y0, h, t1)

Below is my code step bby by step for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

Define RR to be the real numbers, rounding to the nearest number, with 25 bits of precision

RR = RealField(25,rnd='RNDN')

Define t,x,y to be numbers in RR

t,x,y = PolynomialRing(RR,3,"txy").gens()

Define the system of equations

firsteq = y

secondeq = -x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

Define parameters

t0 = 0

x0 = 0

y0 = 2

h = 1/4

n = 10

t1 = t0 + n*h

Plot the x(t) and y(t) graphs

eulers_method_2x2_plot(firsteq , secondeq, t0, x0, y0, h, t1)

Below is my code step by step for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

Define RR to be the real numbers, rounding to the nearest number, with 25 bits of precision

RR = RealField(25,rnd='RNDN')

Define t,x,y to be numbers in RR

t,x,y = PolynomialRing(RR,3,"txy").gens()

Define the system of equations

firsteq = y

secondeq = -x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

Define parameters

t0 = 0

x0 = 0

y0 = 2

h = 1/4

n = 10

t1 = t0 + n*h

Plot the x(t) and y(t) graphs

eulers_method_2x2_plot(firsteq , secondeq, t0, x0, y0, h, t1)

Below is my code step by step for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

Below is my code step by step for using Euler's Method to approximate a solution of a system. It will work when n = 10, but not when n = 100 or 1000. How can I fix it so that the output isn't truncated. Thanks!

# Define RR to be the real numbers, rounding to the nearest number, with 25 bits of precision
RR = RealField(25,rnd='RNDN')

# Define t,x,y to be numbers in RR
t,x,y = PolynomialRing(RR,3,"txy").gens()

# Define the system of equations
firsteq = y

secondeq = -x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

# Define parameters
t0 = 0 

x0 = 0

y0 = 2

h = 1/4

n = 10

t1 = t0 + n*h


# Plot the x(t) and y(t) graphs
eulers_method_2x2_plot(firsteq , secondeq, t0, x0, y0, h, t1)