NAG Library Function Document

nag_ode_ivp_rk_interp (d02pxc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     neq – IntegerInput

On entry: the number of ordinary differential equations in the system.

Constraint: $\mathbf{neq}\ge 1$.

2:     twant – doubleInput

On entry: the value of the independent variable, $t$, where a solution is desired.

3:     request – Nag_SolDerivInput

On entry: determines whether the solution and/or its first derivative are computed as follows:

• $\mathbf{request}=\mathrm{Nag\_Sol}$ – compute approximate solution only;
• $\mathbf{request}=\mathrm{Nag\_Der}$ – compute approximate first derivative of the solution only;
• $\mathbf{request}=\mathrm{Nag\_SolDer}$ – compute both approximate solution and first derivative.

Constraint: $\mathbf{request}=\mathrm{Nag\_Sol}$, $\mathrm{Nag\_Der}$ or $\mathrm{Nag\_SolDer}$.

4:     nwant – IntegerInput

On entry: the number of components of the solution to be computed. The first nwant components are evaluated.

Constraint: $1\le \mathbf{nwant}\le \mathbf{neq}$.

5:     ywant[nwant] – doubleOutput

On exit: an approximation to the first nwant components of the solution at twant when specified by request.

6:     ypwant[nwant] – doubleOutput

On exit: an approximation to the first nwant components of the first derivative of the solution at twant when specified by request.

7:     f – function, supplied by the userExternal Function

f must evaluate the functions $f_i$ (that is the first derivatives $y_i^{\prime }$) for given values of the arguments $t,y_i$. It must be the same procedure as supplied to nag_ode_ivp_rk_onestep (d02pdc).

The specification of f is:

void  f (Integer neq, double t, const double y[], double yp[], Nag_User *comm)

1:     neq – IntegerInput

On entry: the number of differential equations.

2:     t – doubleInput

On entry: the current value of the independent variable, t.

3:     y[neq] – const doubleInput

On entry: the current values of the dependent variables, $y_i$ for $i=1,2,\dots ,\mathbf{neq}$.

4:     yp[neq] – doubleOutput

On exit: the values of $f_i$ for $i=1,2,\dots ,\mathbf{neq}$.

5:     comm – Nag_User *

Pointer to a structure of type Nag_User with the following member:

p – Pointer 

On entry/exit: the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$ should be cast to the required type, e.g., struct user *s = (struct user *)comm → p, to obtain the original object's address with appropriate type. (See the argument comm below.)

8:     opt – Nag_ODE_RK *Input/Output

On entry: the structure of type Nag_ODE_RK as output from nag_ode_ivp_rk_onestep (d02pdc). You must not change this structure.

On exit: some members of opt are changed internally.

9:     comm – Nag_User *

Pointer to a structure of type Nag_User with the following member:

p – Pointer 

On entry/exit: the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$, of type Pointer, allows you to communicate information to and from f. An object of the required type should be declared, e.g., a structure, and its address assigned to the pointer $\mathbf{comm}\mathbf{\to }\mathbf{p}$ by means of a cast to Pointer in the calling program, e.g., comm.p = (Pointer)&s. The type pointer will be void * with a C compiler that defines void * and char * otherwise.

10:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_2_INT_ARG_GT

On entry, $\mathbf{nwant}=⟨\mathit{\text{value}}⟩$ while $\mathbf{neq}=⟨\mathit{\text{value}}⟩$. These arguments must satisfy $\mathbf{neq}\le \mathbf{nwant}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument request had an illegal value.

NE_INT_ARG_LT

On entry, $\mathbf{nwant}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{nwant}\ge 1$.

NE_MEMORY_FREED

Internally allocated memory has been freed by a call to nag_ode_ivp_rk_free (d02ppc) without a subsequent call to the setup function nag_ode_ivp_rk_setup (d02pvc).

NE_MISSING_CALL

Previous call to nag_ode_ivp_rk_onestep (d02pdc) has not been made, hence nag_ode_ivp_rk_interp (d02pxc) must not be called.

NE_NEQ

The value of neq supplied is not the same as that given to the setup function nag_ode_ivp_rk_setup (d02pvc). $\mathbf{neq}=⟨\mathit{\text{value}}⟩$ but the value given to nag_ode_ivp_rk_setup (d02pvc) was $⟨\mathit{\text{value}}⟩$.

NE_PREV_CALL

The previous call to a function had resulted in a severe error. You must call nag_ode_ivp_rk_setup (d02pvc) to start another problem.

NE_PREV_CALL_INI

The previous call to the function nag_ode_ivp_rk_onestep (d02pdc) resulted in a severe error. You must call nag_ode_ivp_rk_setup (d02pvc) to start another problem.

NE_RK_INVALID_CALL

The function to be called as specified in the setup function nag_ode_ivp_rk_setup (d02pvc) was nag_ode_ivp_rk_range (d02pcc). However the actual call was made to nag_ode_ivp_rk_interp (d02pxc). This is not permitted.

NE_RK_PX_METHOD

Interpolation is not available with $\mathbf{method}=\mathrm{Nag\_RK\_7\_8}$. Either use $\mathbf{method}=\mathrm{Nag\_RK\_2\_3}$ or $\mathrm{Nag\_RK\_4\_5}$ for which interpolation is available. Alternatively use nag_ode_ivp_rk_reset_tend (d02pwc) to make nag_ode_ivp_rk_onestep (d02pdc) step exactly to the points where you want output.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (d02pxce.c)

10.2  Program Data

10.3  Program Results

Program Results (d02pxce.r)