# getExactSolution Compare analytical and calculated solutions ```r getExactSolution(object, t, ...) ``` ## Arguments - `object`: a class object - `t`: time ath what we are performing the evaluation - `...`: additional parameters ## Examples ```r # ++++++++++++++++++++++++++++++++++++++++++++++++ example: ComparisonRK45App.R # Compares the solution by the RK45 ODE solver versus the analytical solution # Example file: ComparisonRK45App.R # ODE Solver: Runge-Kutta 45 # ODE class : RK45 # Base class: ODETest importFromExamples("ODETest.R") ComparisonRK45App <- function(verbose = FALSE) { ode <- new("ODETest") # create an `ODETest` object ode_solver <- RK45(ode) # select the ODE solver ode_solver <- setStepSize(ode_solver, 1) # set the step # Two ways of setting the tolerance # ode_solver <- setTolerance(ode_solver, 1e-8) # set the tolerance setTolerance(ode_solver) <- 1e-8 time <- 0 rowVector <- vector("list") i <- 1 while (time < 50) { rowVector[[i]] <- list(t = getState(ode)[2], s1 = getState(ode)[1], s2 = getState(ode)[2], xs = getExactSolution(ode, time), counts = getRateCounts(ode), time = time ) ode_solver <- step(ode_solver) # advance one step stepSize <- getStepSize(ode_solver) time <- time + stepSize ode <- getODE(ode_solver) # get updated ODE object i <- i + 1 } return(data.table::rbindlist(rowVector)) # a data table with the results } # show solution solution <- ComparisonRK45App() # run the example plot(solution) # ODETest.R # Called as base class for examples: # ComparisonRK45App.R # ComparisonRK45ODEApp.R #' ODETest as an example of ODE class inheritance #' #' ODETest is a base class for examples ComparisonRK45App.R and #' ComparisonRK45ODEApp.R. ODETest also uses an environment variable to store #' the rate counts. #' #' @rdname ODE-class-example #' @include ODE.R setClass("ODETest", slots = c( n = "numeric", # counts the number of getRate evaluations stack = "environment" # environnment object to accumulate rate counts ), contains = c("ODE") ) setMethod("initialize", "ODETest", function(.Object, ...) { .Object@stack$rateCounts <- 0 # counter for rate calculations .Object@state <- c(5.0, 0.0) return(.Object) }) #' @rdname getExactSolution-method setMethod("getExactSolution", "ODETest", function(object, t, ...) { return(5.0 * exp(-t)) }) #' @rdname getState-method setMethod("getState", "ODETest", function(object, ...) { object@state }) #' @rdname getRate-method setMethod("getRate", "ODETest", function(object, state, ...) { object@rate[1] <- - state[1] object@rate[2] <- 1 # rate of change of time, dt/dt # accumulate how many times the rate has been called to calculate object@stack$rateCounts <- object@stack$rateCounts + 1 object@state <- state object@rate }) #' @rdname getRateCounts-method setMethod("getRateCounts", "ODETest", function(object, ...) { # use environment stack to accumulate rate counts object@stack$rateCounts }) # constructor ODETest <- function() { odetest <- new("ODETest") odetest } ```

getExactSolution-method function