If Matlabįinds several solutions it returns a vector of solutions. If Matlab can't find a solution it will return an empty symbol. The last argument 't' is the name of the independent variable. Y for y( t): E.g., for the differential equation You have to specify the differential equation in a Solving a differential equation symbolically ode15s is also better at detecting whereĪ solution stops to exist if the slope becomes infinite. This happens for so-called stiff problems. Note that in some cases ode15s performs better than ode45. In this case ode45 prints a warning " Failure at t=." to show where it stopped. It may happen that the solution does not exist on the whole interval: To obtain the numerical value of the solution at the final , 1.5, 2 andĭisplay the results as a table with two columns, use With the initial condition y(-2)=1 at t = -2, -1.5. Theįirst element of the vector tv is the initial t value the vector To obtain numerical values of the solution atĬertain t values: You can specify a vector tv of t After the last plot command type hold off.Įxample: Plot the direction field and the 13 solution curves with The first plot type hold on, then all subsequent commands plot in To combine plots of the direction field and several The solution without the circles using plot(ts,ys). Ts and ys contain the coordinates of these points, to see them The circles mark the values which were actually computed (the points areĬhosen by Matlab to optimize accuracy and efficiency). Problem: For the initial condition y(t0)=y0 you can plot theĮxample: To plot the solution of the initial value problem To plot the numerical solution of an initial value Right hand side of the differential equation y'( t) = T and y between -2 and 2 with a spacing of 0.2ĭirfield(f,-2:0.2:2,-2:0.2:2) Solving an initial value problem numerically Hand side of the differential equation y'( t) =Į.g., for the ODE y'=y 2 you would use plot the direction field for t going from t0 to t1 withĪ spacing of dt and y going from y0 to y1 with a spacing of dy use Of two variables t, y corresponding to the right The same directory as your other m-files for the homework. make a contour plot of the function for a rectangle in the x,y plane:Įzcontour(G,) colorbar Direction Fieldsįirst download the file dirfield.m and put it in.plot the curves where G(x,y)=0 in a rectangle in the x,y plane:.plot the graph of the function as a surface over a rectangle in the x,y plane:Ĭlick on in the figure toolbar, then you can rotate the.evaluate the function for given values of x,y:.G(x,y) = x 4 + y 4 - 4(x 2 + y 2) + 4 of two variables. You can also define of several variables:
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