Merge pull request #8 from kleo-53/task7

Задания 7 и 8: решение краевой задачи различными методами.
kleo-53 · May 8, 2024 · 047c0a6 · 047c0a6
2 parents 5a9c181 + b394c8d
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diff --git a/task7/8-nets.png b/task7/8-nets.png
diff --git a/task7/8-newCollocation.png b/task7/8-newCollocation.png
diff --git a/task7/8-ritz.png b/task7/8-ritz.png
diff --git a/task7/deltas.png b/task7/deltas.png
diff --git a/task7/functions.png b/task7/functions.png
diff --git a/task7/go.mod b/task7/go.mod
@@ -0,0 +1,14 @@
+module workshop/task7
+
+go 1.22.1
+
+require (
+	github.com/wcharczuk/go-chart/v2 v2.1.1
+	gonum.org/v1/gonum v0.15.0
+)
+
+require (
+	github.com/blend/go-sdk v1.20220411.3 // indirect
+	github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 // indirect
+	golang.org/x/image v0.14.0 // indirect
+)
diff --git a/task7/go.sum b/task7/go.sum
@@ -0,0 +1,44 @@
+github.com/blend/go-sdk v1.20220411.3 h1:GFV4/FQX5UzXLPwWV03gP811pj7B8J2sbuq+GJQofXc=
+github.com/blend/go-sdk v1.20220411.3/go.mod h1:7lnH8fTi6U4i1fArEXRyOIY2E1X4MALg09qsQqY1+ak=
+github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 h1:DACJavvAHhabrF08vX0COfcOBJRhZ8lUbR+ZWIs0Y5g=
+github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0/go.mod h1:E/TSTwGwJL78qG/PmXZO1EjYhfJinVAhrmmHX6Z8B9k=
+github.com/wcharczuk/go-chart/v2 v2.1.1 h1:2u7na789qiD5WzccZsFz4MJWOJP72G+2kUuJoSNqWnE=
+github.com/wcharczuk/go-chart/v2 v2.1.1/go.mod h1:CyCAUt2oqvfhCl6Q5ZvAZwItgpQKZOkCJGb+VGv6l14=
+github.com/yuin/goldmark v1.4.13/go.mod h1:6yULJ656Px+3vBD8DxQVa3kxgyrAnzto9xy5taEt/CY=
+golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
+golang.org/x/crypto v0.0.0-20210921155107-089bfa567519/go.mod h1:GvvjBRRGRdwPK5ydBHafDWAxML/pGHZbMvKqRZ5+Abc=
+golang.org/x/exp v0.0.0-20231110203233-9a3e6036ecaa h1:FRnLl4eNAQl8hwxVVC17teOw8kdjVDVAiFMtgUdTSRQ=
+golang.org/x/exp v0.0.0-20231110203233-9a3e6036ecaa/go.mod h1:zk2irFbV9DP96SEBUUAy67IdHUaZuSnrz1n472HUCLE=
+golang.org/x/image v0.11.0/go.mod h1:bglhjqbqVuEb9e9+eNR45Jfu7D+T4Qan+NhQk8Ck2P8=
+golang.org/x/image v0.14.0 h1:tNgSxAFe3jC4uYqvZdTr84SZoM1KfwdC9SKIFrLjFn4=
+golang.org/x/image v0.14.0/go.mod h1:HUYqC05R2ZcZ3ejNQsIHQDQiwWM4JBqmm6MKANTp4LE=
+golang.org/x/mod v0.6.0-dev.0.20220419223038-86c51ed26bb4/go.mod h1:jJ57K6gSWd91VN4djpZkiMVwK6gcyfeH4XE8wZrZaV4=
+golang.org/x/mod v0.8.0/go.mod h1:iBbtSCu2XBx23ZKBPSOrRkjjQPZFPuis4dIYUhu/chs=
+golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
+golang.org/x/net v0.0.0-20210226172049-e18ecbb05110/go.mod h1:m0MpNAwzfU5UDzcl9v0D8zg8gWTRqZa9RBIspLL5mdg=
+golang.org/x/net v0.0.0-20220722155237-a158d28d115b/go.mod h1:XRhObCWvk6IyKnWLug+ECip1KBveYUHfp+8e9klMJ9c=
+golang.org/x/net v0.6.0/go.mod h1:2Tu9+aMcznHK/AK1HMvgo6xiTLG5rD5rZLDS+rp2Bjs=
+golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.1.0/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
+golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
+golang.org/x/sys v0.0.0-20210615035016-665e8c7367d1/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.0.0-20220520151302-bc2c85ada10a/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.0.0-20220722155257-8c9f86f7a55f/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/sys v0.5.0/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
+golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
+golang.org/x/term v0.0.0-20210927222741-03fcf44c2211/go.mod h1:jbD1KX2456YbFQfuXm/mYQcufACuNUgVhRMnK/tPxf8=
+golang.org/x/term v0.5.0/go.mod h1:jMB1sMXY+tzblOD4FWmEbocvup2/aLOaQEp7JmGp78k=
+golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
+golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
+golang.org/x/text v0.3.7/go.mod h1:u+2+/6zg+i71rQMx5EYifcz6MCKuco9NR6JIITiCfzQ=
+golang.org/x/text v0.7.0/go.mod h1:mrYo+phRRbMaCq/xk9113O4dZlRixOauAjOtrjsXDZ8=
+golang.org/x/text v0.12.0/go.mod h1:TvPlkZtksWOMsz7fbANvkp4WM8x/WCo/om8BMLbz+aE=
+golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
+golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
+golang.org/x/tools v0.1.12/go.mod h1:hNGJHUnrk76NpqgfD5Aqm5Crs+Hm0VOH/i9J2+nxYbc=
+golang.org/x/tools v0.6.0/go.mod h1:Xwgl3UAJ/d3gWutnCtw505GrjyAbvKui8lOU390QaIU=
+golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
+gonum.org/v1/gonum v0.15.0 h1:2lYxjRbTYyxkJxlhC+LvJIx3SsANPdRybu1tGj9/OrQ=
+gonum.org/v1/gonum v0.15.0/go.mod h1:xzZVBJBtS+Mz4q0Yl2LJTk+OxOg4jiXZ7qBoM0uISGo=
diff --git a/task7/main.go b/task7/main.go
@@ -0,0 +1,78 @@
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+// коэффициент при u”
+func p(x float64) float64 {
+	return -(5.0 - x) / (7.0 - 3.0*x)
+}
+
+// коэффициент при u'
+func q(x float64) float64 {
+	return -(1.0 - x) / 2.0
+}
+
+// коэффициент при u
+func r(x float64) float64 {
+	return 1.0 + 0.5*math.Sin(x)
+}
+
+// правая часть дифференциального уравнения
+func f(x float64) float64 {
+	return 0.5 + x/2.0
+}
+
+// ___
+// коэффициент при y'
+func p8(x float64) float64 {
+	return (2.0 + x) / (3.0 + x)
+}
+
+// коэффициент при y
+func r8(x float64) float64 {
+	return 1.0 + math.Sin(x)
+}
+
+func q8(float64) float64 {
+	return 0.0
+}
+
+// правая часть дифференциального уравнения
+func f8(x float64) float64 {
+	return 1.0 - x
+}
+
+func main() {
+	var task int
+	fmt.Scanf("%d\n", &task)
+	if task == 7 {
+		a, b, typeF, eps, alpha1, alpha2, alpha, beta1, beta2, beta := -1.0, 1.0, 1, 1e-4, 0.0, 1.0, 0.0, 3.0, 2.0, 0.0
+		x_d, net_d, delta_d, n_d := solveTask(p, q, r, f, a, b, typeF, eps, alpha1, alpha2, alpha, beta1, beta2, beta)
+		fmt.Println("Variant 10. Approximation results are in 'nets.png' and 'deltas.png'")
+		drowGraphic(x_d, net_d, n_d, "nets")
+		drowGraphic(x_d, delta_d, n_d, "deltas")
+	} else {
+		alpha1, alpha2, beta1, beta2 := 0.0, 1.0, 1.0, 1.0
+		typeF := 0
+		if alpha1*alpha2*beta1*beta2 != 0 {
+			typeF = 3
+		}
+		if alpha1*alpha2 != 0 {
+			typeF = 1
+		}
+		if beta2*beta2 != 0 {
+			typeF = 2
+		}
+		a, b, eps, alpha, beta := -1.0, 1.0, 2e-4, 0.0, 0.0
+		x_d, net_d, _, n_d := solveTask(p8, q8, r8, f8, a, b, 2, eps, alpha1, alpha2, alpha, beta1, beta2, beta)
+		fmt.Println("Сравнение с методом сеток. Результат в '8-nets.png'")
+		drowGraphic(x_d, net_d, n_d, "8-nets")
+		fmt.Println("Вычисляем методом Ритца при разных n. Результат в '8-ritz.png'")
+		solveRitz(p8, r8, f8, typeF, alpha1, alpha2, beta1, beta2)
+		fmt.Println("Вычисляем методом коллокации при разных n. Результат в '8-newCollocation.png'")
+		solveCol(p8, r8, f8)
+	}
+}
diff --git a/task7/nets.png b/task7/nets.png
diff --git a/task7/newCollocation.go b/task7/newCollocation.go
@@ -0,0 +1,94 @@
+package main
+
+import (
+	"gonum.org/v1/gonum/mat"
+)
+
+func wi(_ float64, i int) Funct {
+	a := Funct{func(x float64) float64 {
+		return (1.0 - x*x) * (1.0 - x*x)
+	}}
+	return a.Mul(Funct{getP(2, i-2)})
+}
+
+func wpi(_ float64, i int) Funct {
+	a := Funct{func(x float64) float64 {
+		return -2.0 * (float64(i) - 1.0) * (1.0 - x*x) * (1.0 - x*x)
+	}}
+	return a.Mul(Funct{getP(1, i-1)})
+}
+
+func wppi(_ float64, i int) Funct {
+	a := Funct{func(float64) float64 {
+		return 4.0 * (float64(i) - 1.0) * float64(i)
+	}}
+	return a.Mul(Funct{getP(0, i)})
+}
+
+func getW(n int) [][]Funct {
+	res := make([][]Funct, n+1)
+	res[0] = []Funct{{func(x float64) float64 {
+		return x*x + 2.0*x - 7.0
+	}}, {func(x float64) float64 {
+		return 2.0*x + 2.0
+	}}, {func(float64) float64 {
+		return 2.0
+	}}}
+	res[1] = []Funct{{func(x float64) float64 {
+		return x*x*x - 3.0*x + 2.0
+	}}, {func(x float64) float64 {
+		return 3.0*x*x - 3.0
+	}}, {func(x float64) float64 {
+		return 6.0 * x
+	}}}
+
+	for i := 2; i < n+1; i++ {
+		res[i] = []Funct{{func(x float64) float64 {
+			return wi(x, i).f(x)
+		}}, {func(x float64) float64 {
+			return wpi(x, i).f(x)
+		}}, {func(x float64) float64 {
+			return wppi(x, i).f(x)
+		}}}
+	}
+	return res
+}
+
+func solveCol(p, r, f func(float64) float64) {
+	xrand := make([][]float64, 5)
+	frand := make([][]float64, 5)
+	ns := make([]int, 5)
+	ind := 0
+	for n := 4; n < 14; n += 2 {
+		xrand[ind] = makeNet(-1, 1, n*10)
+		dots := makeNet(-1, 1, n)
+		a := mat.NewDense(n+1, n+1, nil)
+		b := mat.NewVecDense(n+1, nil)
+		coord := getW(n)
+		for i := 0; i < n+1; i++ {
+			x := dots[i]
+			for j := 0; j < n+1; j++ {
+				a.Set(i, j, -p(x)*coord[j][2].f(x)+q(x)*coord[j][1].f(x)+r(x)*coord[j][0].f(x))
+			}
+			b.SetVec(i, f(x))
+		}
+		res := mat.NewVecDense(n+1, nil)
+		res.SolveVec(a, b)
+		y := Funct{func(x float64) float64 {
+			return 0.0
+		}}
+		for i := 0; i < n+1; i++ {
+			fa := Funct{func(x float64) float64 {
+				return res.AtVec(i) * coord[i][0].f(x)
+			}}
+			y = y.Add(fa)
+		}
+		frand[ind] = make([]float64, n*10+1)
+		for i := 0; i < n*10+1; i++ {
+			frand[ind][i] = y.f(xrand[ind][i])
+		}
+		ns[ind] = n + 1
+		ind++
+	}
+	drowGraphic(xrand, frand, ns, "8-newCollocation")
+}