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}, "execution_count": 1, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ] }, "execution_count": 1, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ] }, "execution_count": 1, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ] }, "execution_count": 1, "metadata": { }, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "WARNING: Some output was deleted.\n" ] } ], "source": [ "def picard_iteration(f, a, c, N):\n", " '''\n", " Computes the N-th Picard iterate for the IVP \n", "\n", " x' = f(t,x), x(a) = c.\n", "\n", " EXAMPLES:\n", " sage: var('x t s')\n", " (x, t, s)\n", " sage: a = 0; c = 2\n", " sage: f = lambda t,x: 1-x\n", " sage: picard_iteration(f, a, c, 0)\n", " 2\n", " sage: picard_iteration(f, a, c, 1)\n", " 2 - t\n", " sage: picard_iteration(f, a, c, 2)\n", " t^2/2 - t + 2\n", " sage: picard_iteration(f, a, c, 3)\n", " -t^3/6 + t^2/2 - t + 2\n", " sage: var('x t s')\n", " (x, t, s)\n", " sage: a = 0; c = 2\n", " sage: f = lambda t,x: (x+t)^2\n", " sage: picard_iteration(f, a, c, 0)\n", " 2\n", " sage: picard_iteration(f, a, c, 1)\n", " t^3/3 + 2*t^2 + 4*t + 2\n", " sage: picard_iteration(f, a, c, 2)\n", " t^7/63 + 2*t^6/9 + 22*t^5/15 + 16*t^4/3 + 11*t^3 + 10*t^2 + 4*t + 2\n", "\n", " '''\n", " if N == 0:\n", " return c*t**0\n", " if N == 1:\n", " #print integral(f(s,c*s**0), s, a, t)\n", " x0 = lambda t: c + integral(f(s,c*s**0), s, a, t)\n", " return expand(x0(t))\n", " for i in range(N):\n", " x_old = lambda s: picard_iteration(f, a, c, N-1).subs(t=s)\n", " #print x_old(s)\n", " x0 = lambda t: c + integral(f(s,x_old(s)), s, a, t)\n", " return expand(x0(t))\n", "v=var('x t s')\n", "a = 0; c = 4; N=40; b=8; x1=-5; x2=10;\n", "f = lambda t,x: sin(t)-2*x; assume(t>0) \n", "z=[picard_iteration(f, a, c, i) for i in range(N+1)]\n", "for i in range(N+1):\n", " show(z[i])\n", "from sage.plot.colors import rainbow\n", "c=rainbow(N+1)\n", "where = [x,-2+1.5,b]\n", "p=plot(-1/5*(cos(t)*e^(2*t) - 2*e^(2*t)*sin(t) - 21)*e^(-2*t),where,ymin=x1,ymax=x2,color='gray',gridlines=True) #SoluciĆ³n exacta.\n", "#p+=plot(z[0],where,gridlines=True)\n", "for i in range(1,N+1):\n", " p+=plot(z[i],where,ymin=x1,ymax=x2,color=c[i])\n", "\n", "show(p)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 2, "metadata": { }, "output_type": "execute_result" } ], "source": [ "N=50;b=1\n", "from sage.plot.colors import rainbow\n", "c=rainbow(N+1)\n", "where = [x,0,b]\n", "p=plot(x^0,where,color='gray',gridlines=True)\n", "for i in range(1,N+1):\n", " p+=plot(x^i,where,color=c[i])\n", "show(p)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" } ], "source": [ "x = var('x')\n", "y = function('y')(x)\n", "show(desolve(diff(y,x) - exp(x+y), y))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" } ], "source": [ "x = var('x')\n", "y = function('y')(x)\n", "f = desolve(diff(y,x) -exp(x+y), y, ics=[0,1]); show(f)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "-1/5*(cos(t)*e^(2*t) - 2*e^(2*t)*sin(t) - 21)*e^(-2*t)" ] }, "execution_count": 5, "metadata": { }, "output_type": "execute_result" } ], "source": [ "t = var('t')\n", "x = function('x')(t)\n", "f = desolve(diff(x,t) -sin(t) + 2*x, x, ics=[0,4]); f" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ] }, "execution_count": 6, "metadata": { }, "output_type": "execute_result" } ], "source": [ "t = var('t')\n", "x = function('x')(t)\n", "f = desolve(diff(x,t) -sin(t) + 2*x, x, ics=[0,4]); show(f)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" } ], "source": [ "def picard_iteration(f, a, c, N):\n", " '''\n", " Computes the N-th Picard iterate for the IVP \n", "\n", " x' = f(t,x), x(a) = c.\n", "\n", " EXAMPLES:\n", " sage: var('x t s')\n", " (x, t, s)\n", " sage: a = 0; c = 2\n", " sage: f = lambda t,x: 1-x\n", " sage: picard_iteration(f, a, c, 0)\n", " 2\n", " sage: picard_iteration(f, a, c, 1)\n", " 2 - t\n", " sage: picard_iteration(f, a, c, 2)\n", " t^2/2 - t + 2\n", " sage: picard_iteration(f, a, c, 3)\n", " -t^3/6 + t^2/2 - t + 2\n", " sage: var('x t s')\n", " (x, t, s)\n", " sage: a = 0; c = 2\n", " sage: f = lambda t,x: (x+t)^2\n", " sage: picard_iteration(f, a, c, 0)\n", " 2\n", " sage: picard_iteration(f, a, c, 1)\n", " t^3/3 + 2*t^2 + 4*t + 2\n", " sage: picard_iteration(f, a, c, 2)\n", " t^7/63 + 2*t^6/9 + 22*t^5/15 + 16*t^4/3 + 11*t^3 + 10*t^2 + 4*t + 2\n", "\n", " '''\n", " if N == 0:\n", " return c*t**0\n", " if N == 1:\n", " #print integral(f(s,c*s**0), s, a, t)\n", " assume(s>0) \n", " x0 = lambda t: c + integral(f(s,c*s**0), s, a, t)\n", " return expand(x0(t))\n", " for i in range(N):\n", " x_old = lambda s: picard_iteration(f, a, c, N-1).subs(t=s)\n", " #print x_old(s)\n", " x0 = lambda t: c + integral(f(s,x_old(s)), s, a, t)\n", " return expand(x0(t))\n", "v=var('x t s')\n", "a = 0; c = 1; N=2; b=.5;\n", "f = lambda t,x: exp(x+t); assume(t>0) \n", "z=[picard_iteration(f, a, c, i) for i in range(N+1)]\n", "for i in range(N+1):\n", " show(z[i])\n", "from sage.plot.colors import rainbow\n", "c=rainbow(N+1)\n", "where = [x,-b,b]\n", "p=plot(-log(abs(-1-exp(-1)+exp(t))),where,color='gray',gridlines=True) #SoluciĆ³n exacta.\n", "#p+=plot(z[0],where,gridlines=True)\n", "for i in range(N+1):\n", " p+=plot(z[i],where,color=c[i])\n", "\n", "show(p)" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ ] } ], "metadata": { "kernelspec": { "display_name": "SageMath (stable)", "language": "sagemath", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 0 }