# odesolv: Numerical Solution mth Order Differential Equation System In fda: Functional Data Analysis

 odesolv R Documentation

## Numerical Solution mth Order Differential Equation System

### Description

The system of differential equations is linear, with possibly time-varying coefficient functions. The numerical solution is computed with the Runge-Kutta method.

### Usage

``````odesolv(bwtlist, ystart=diag(rep(1,norder)),
h0=width/100, hmin=width*1e-10, hmax=width*0.5,
EPS=1e-4, MAXSTP=1000)
``````

### Arguments

 `bwtlist` a list whose members are functional parameter objects defining the weight functions for the linear differential equation. `ystart` a vector of initial values for the equations. These are the values at time 0 of the solution and its first m - 1 derivatives. `h0` a positive initial step size. `hmin` the minimum allowable step size. `hmax` the maximum allowable step size. `EPS` a convergence criterion. `MAXSTP` the maximum number of steps allowed.

### Details

This function is required to compute a set of solutions of an estimated linear differential equation in order compute a fit to the data that solves the equation. Such a fit will be a linear combinations of m independent solutions.

### Value

a named list of length 2 containing

 `tp` a vector of time values at which the system is evaluated `yp` a matrix of variable values corresponding to `tp`.

### References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

`pda.fd`. For new applications, users are encouraged to consider `deSolve`. The `deSolve` package provides general solvers for ordinary and partial differential equations, as well as differential algebraic equations and delay differential equations.
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