fixes for SolveIVP implementation

ode/ivp_test.go

@@ -82,8 +82,24 @@ func Example_solve() {
 	// Solve function makes it easy to integrate a problem without having
 	// to implement the `for` loop. This example integrates the IVP with a step size
 	// of 0.1 over a domain of 10. arbitrary units, in this case, 10 seconds.
-	results, err := ode.SolveIVP(ballModel, solver, 0.1, 10.)
-	fmt.Println(results)
+	results, err := ode.SolveIVP(ballModel, solver, 0.5, 5.)
+	for _, state := range results {
+		t := state.T
+		y := state.Y
+		fmt.Printf("time=%0.3g, position=%0.3g, velocity=%0.3g\n", t, y.AtVec(0), y.AtVec(1))
+	}
+	//Output:
+	// time=0, position=100, velocity=0
+	// time=0.5, position=98.8, velocity=-5
+	// time=1, position=95, velocity=-10
+	// time=1.5, position=88.8, velocity=-15
+	// time=2, position=80, velocity=-20
+	// time=2.5, position=68.8, velocity=-25
+	// time=3, position=55, velocity=-30
+	// time=3.5, position=38.8, velocity=-35
+	// time=4, position=20, velocity=-40
+	// time=4.5, position=-1.25, velocity=-45
+	// time=5, position=-25, velocity=-50
 }
 
 // Quadratic model may be used for future algorithms
@@ -113,9 +129,10 @@ func quadTestModel(t *testing.T) *TestModel {
 }
 
 // exponential unidimensional model may be used for future algorithms
-//  y'(t) = -15*y(t)
-//  y(t=0) = 1
-//  solution: y(t) = exp(-15*t)
+//
+//	y'(t) = -15*y(t)
+//	y(t=0) = 1
+//	solution: y(t) = exp(-15*t)
 func exp1DTestModel(t *testing.T) *TestModel {
 	tau := -2.
 	t0 := 0.0

ode/ode.go

@@ -11,6 +11,8 @@ import (
 	"gonum.org/v1/gonum/mat"
 )
 
+var errNegativeStepSize = errors.New("ode: got zero or negative step size from Integrator")
+
 // Integrator can integrate an initial-value problem (IVP) for a first-order
 // system of ordinary differential equations (ODEs).
 type Integrator interface {
@@ -46,10 +48,12 @@ func SolveIVP(p IVP, solver Integrator, stepsize, tend float64) (results []State
 	if nx == 0 {
 		return nil, errors.New("state vector length can not be equal to zero. Has ivp been set?")
 	}
+	solver.Init(p)
 	// calculate expected size of results, these may differ
 	domainLength := tend - t0
 	expectedLength := int(domainLength/stepsize) + 1
 	results = make([]State, 0, expectedLength)
+	results = append(results, State{T: t0, Y: x0}) // append initial condition.
 
 	// t stores current domain
 	t := t0
@@ -64,7 +68,7 @@ func SolveIVP(p IVP, solver Integrator, stepsize, tend float64) (results []State
 			return results, err
 		}
 		if stepsize <= 0 {
-			return results, errors.New("got zero or negative step size from Integrator")
+			return results, errNegativeStepSize
 		}
 		solver.State(&res)
 		t += stepsize