Documentation improvements: Fix typos, bugs, and inconsistencies

- Fix typo: "Google Collab" → "Google Colab"
- Fix typo: "tolernace" → "tolerance"
- Fix critical bug in DDE example: constant_lags was incorrectly assigned tspan value
- Fix tspan inconsistencies: Changed list() to c() in vignettes (ode.Rmd, sde.Rmd)
- Standardize pipe operators: Updated %>% to |> (native R 4.1+ pipe) in dae.Rmd and dde.Rmd
- Add missing interpolation code example in ode.Rmd (sol$.(0.2))

These changes improve documentation accuracy and consistency across README and vignettes.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

Author: claude

README.md

@@ -35,7 +35,7 @@ make sure that `julia` is found in the path. For more
 information see the `julia_setup()` function from
 [JuliaCall](https://github.com/JuliaInterop/JuliaCall).
 
-## Google Collab Notebooks
+## Google Colab Notebooks
 
 As a demonstration, check out the following notebooks:
 
@@ -162,7 +162,7 @@ Plotly is much prettier!
 
 If we want to have a more accurate solution, we can send `abstol` and `reltol`. Defaults are `1e-6` and `1e-3` respectively.
 Generally you can think of the digits of accuracy as related to 1 plus the exponent of the relative tolerance, so the default is
-two digits of accuracy. Absolute tolernace is the accuracy near 0.
+two digits of accuracy. Absolute tolerance is the accuracy near 0.
 
 In addition, we may want to choose to save at more time points. We do this by giving an array of values to save at as `saveat`.
 Together, this looks like:
@@ -458,7 +458,7 @@ tspan <- c(0.0, 100.0)
 constant_lags <- c(20.0)
 JuliaCall::julia_assign("u0", u0)
 JuliaCall::julia_assign("tspan", tspan)
-JuliaCall::julia_assign("constant_lags", tspan)
+JuliaCall::julia_assign("constant_lags", constant_lags)
 prob <- JuliaCall::julia_eval("DDEProblem(f, u0, h, tspan, constant_lags = constant_lags)")
 sol <- de$solve(prob,de$MethodOfSteps(de$Tsit5()))
 udf <- as.data.frame(t(sapply(sol$u,identity)))

vignettes/dae.Rmd

@@ -39,8 +39,8 @@ differential_vars <- c(TRUE,TRUE,FALSE)
 prob <- de$DAEProblem(f,du0,u0,tspan,differential_vars=differential_vars)
 sol <- de$solve(prob)
 udf <- as.data.frame(t(sapply(sol$u,identity)))
-plotly::plot_ly(udf, x = sol$t, y = ~V1, type = 'scatter', mode = 'lines') %>%
-  plotly::add_trace(y = ~V2) %>%
+plotly::plot_ly(udf, x = sol$t, y = ~V1, type = 'scatter', mode = 'lines') |>
+  plotly::add_trace(y = ~V2) |>
   plotly::add_trace(y = ~V3)
 ```
 

vignettes/dde.Rmd

@@ -39,11 +39,11 @@ tspan <- c(0.0, 100.0)
 constant_lags <- c(20.0)
 JuliaCall::julia_assign("u0", u0)
 JuliaCall::julia_assign("tspan", tspan)
-JuliaCall::julia_assign("constant_lags", tspan)
+JuliaCall::julia_assign("constant_lags", constant_lags)
 prob <- JuliaCall::julia_eval("DDEProblem(f, u0, h, tspan, constant_lags = constant_lags)")
 sol <- de$solve(prob,de$MethodOfSteps(de$Tsit5()))
 udf <- as.data.frame(t(sapply(sol$u,identity)))
-plotly::plot_ly(udf, x = sol$t, y = ~V1, type = 'scatter', mode = 'lines') %>% plotly::add_trace(y = ~V2)
+plotly::plot_ly(udf, x = sol$t, y = ~V1, type = 'scatter', mode = 'lines') |> plotly::add_trace(y = ~V2)
 ```
 
 ![delay](https://user-images.githubusercontent.com/1814174/39023532-10bdd750-43f0-11e8-837d-156d33ea2f99.png)

vignettes/ode.Rmd

@@ -50,6 +50,10 @@ This gives back a solution object for which `sol$t` are the time points
 and `sol$u` are the values. We can treat the solution as a continuous object
 in time via
 
+```R
+sol$.(0.2)
+```
+
 and a high order interpolation will compute the value at `t=0.2`. We can check
 the solution by plotting it:
 
@@ -77,7 +81,7 @@ Here we utilized the parameter array `p`. Thus we use `diffeqr::ode.solve` like
 
 ```R
 u0 <- c(1.0,0.0,0.0)
-tspan <- list(0.0,100.0)
+tspan <- c(0.0,100.0)
 p <- c(10.0,28.0,8/3)
 prob <- de$ODEProblem(f, u0, tspan, p)
 sol <- de$solve(prob)

vignettes/sde.Rmd

@@ -30,7 +30,7 @@ g <- function(u,p,t) {
   return(0.87*u)
 }
 u0 <- 1/2
-tspan <- list(0.0,1.0)
+tspan <- c(0.0,1.0)
 prob <- de$SDEProblem(f,g,u0,tspan)
 sol <- de$solve(prob)
 udf <- as.data.frame(t(sapply(sol$u,identity)))