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SciML · Nov 25, 2024 · aad6081 · aad6081
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diff --git a/README.md b/README.md
@@ -47,7 +47,7 @@ In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` o
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.
-
+  - `SmoothedConstantInterpolation(u,t)` - An integral preserving continuously differentiable approximation of constant interpolation.
   - `LinearInterpolation(u,t)` - A linear interpolation.
   - `QuadraticInterpolation(u,t)` - A quadratic interpolation.
   - `LagrangeInterpolation(u,t,n)` - A Lagrange interpolation of order `n`.

diff --git a/docs/src/index.md b/docs/src/index.md
@@ -17,7 +17,7 @@ In all cases, `u` an `AbstractVector` of values and `t` is an `AbstractVector` o
 corresponding to `(u,t)` pairs.
 
   - `ConstantInterpolation(u,t)` - A piecewise constant interpolation.
-
+  - `SmoothedConstantInterpolation(u,t)` - An integral preserving continuously differentiable approximation of constant interpolation.
   - `LinearInterpolation(u,t)` - A linear interpolation.
   - `QuadraticInterpolation(u,t)` - A quadratic interpolation.
   - `LagrangeInterpolation(u,t,n)` - A Lagrange interpolation of order `n`.

diff --git a/docs/src/manual.md b/docs/src/manual.md
@@ -6,6 +6,7 @@ QuadraticInterpolation
 LagrangeInterpolation
 AkimaInterpolation
 ConstantInterpolation
+SmoothedConstantInterpolation
 QuadraticSpline
 CubicSpline
 BSplineInterpolation

diff --git a/docs/src/methods.md b/docs/src/methods.md
@@ -77,6 +77,24 @@ A = ConstantInterpolation(u, t, dir = :right)
 plot(A)
 ```
 
+## Smoothed Constant Interpolation
+
+This function is much like the constant interpolation above, but the transition
+between consecutive values is smoothed out so that the function is continuously 
+differentiable. The smoothing is done in such a way that the integral of this function
+is never much off from the same integral of constant interpolation without smoothing (because of the symmetry of the smoothing sections).
+The maximum smoothing distance in the `t` direction from the data points can be set
+with the keyword argument `d_max`.
+
+```@example tutorial
+A = ConstantInterpolation(u, t)
+plot(A)
+A = SmoothedConstantInterpolation(u, t; d_max = 10)
+plot!(A)
+```
+
+Note that `u[end]` is ignored.
+
 ## Quadratic Spline
 
 This is the quadratic spline. It is a continuously differentiable interpolation

diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
@@ -290,8 +290,8 @@ end
         cache_parameters = false, assume_linear_t = 1e-2)
 
 It is a method for interpolating constantly with forward fill, with smoothing around the
-value transitions to make the curve C1 smooth while the integral never drifts far from
-the integral of constant interpolation.
+value transitions to make the curve continuously differentiable while the integral never 
+drifts far from the integral of constant interpolation. In this interpolation type u[end] is ignored.
 
 ## Arguments