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KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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KerMor
0.9
Model order reduction for nonlinear dynamical systems and nonlinear approximation
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Explicit forward euler ODE solver. More...
Explicit forward euler ODE solver.
This solver uses the MaxStep property as timestep to be most efficient. Set small enough for precision.
\[ x_{i+1} = x_i + \Delta t f(t_i,x_i)\]
This class is part of the framework
Homepage http://www.morepas.org/software/index.htmlDocumentation http://www.morepas.org/software/kermor/index.htmlLicense KerMor license conditions Definition at line 18 of file ExplEuler.m.
Public Member Functions | |
| ExplEuler (double MaxStep) | |
| Constructor for the explicit euler solver. More... | |
 Public Member Functions inherited from solvers.BaseCustomSolver | |
| BaseCustomSolver () | |
| function [ rowvec t , matrix x ] = | solve (function_handle odefun,rowvec t,colvec x0) |
| Solves the ode and wraps the actual solving method. More... | |
| Public Member Functions inherited from solvers.BaseSolver | |
| BaseSolver () | |
| virtual function [ rowvec t , matrix x ] = | solve (odefun,rowvec t,colvec x0) |
| The abstract solve function for the ODE solver. More... | |
| Public Member Functions inherited from KerMorObject | |
| KerMorObject () | |
| Constructs a new KerMor object. More... | |
| function | display () |
| disp(object2str(this)); More... | |
| function bool = | eq (B) |
| Checks equality of two KerMor objects. More... | |
| function bool = | ne (B) |
| Checks if two KerMorObjects are different. More... | |
| function cn = | getClassName () |
| Returns the simple class name of this object without packages. More... | |
| Public Member Functions inherited from DPCMObject | |
| DPCMObject () | |
| Creates a new DPCM object. More... | |
| DPCMObject () | |
Protected Member Functions | |
| function matrix x = | customSolve (function_handle odefun,rowvec t,colvec x0,rowvec< integer > outputtimes) |
| Solves the ODE using the explicit Euler method. More... | |
| Protected Member Functions inherited from solvers.BaseCustomSolver | |
| virtual function colvec< double > x = | customSolve (odefun, t, x0, outputtimes) |
| The abstract solve function for custom ODE solver implementations. More... | |
| Protected Member Functions inherited from KerMorObject | |
| function | checkType (obj, type) |
| Object typechecker. More... | |
| Protected Member Functions inherited from DPCMObject | |
| function | registerProps (varargin) |
| Call this method at any class that defines DPCM observed properties. More... | |
| function | registerProps (varargin) |
Additional Inherited Members | |
| Static Public Member Functions inherited from solvers.BaseSolver | |
| static function res = | test_SolverSpeedTest () |
| Public Attributes inherited from solvers.BaseCustomSolver | |
| EVENT | PreSolve |
| Gets fired before the solver starts. More... | |
| EVENT | PostSolve |
| Gets fired after the solver has finished. More... | |
| Public Attributes inherited from solvers.BaseSolver | |
| double | MaxStep = "[]" |
| Maximum time step for solver. More... | |
| double | InitialStep = "[]" |
| The initial step size for the solver. So far only used by the MLWrapper class for the native matlab solvers. More... | |
| logical | RealTimeMode = false |
| Determines if the solver's StepPerformed event should be used upon solving instead of returning the full trajectory as one. More... | |
| dscomponents.AMassMatrix | M = "[]" |
| The mass matrix \(M\) of the ODE \(M(t)x'(t) = \ldots\). More... | |
| Name = "KerMor BaseSolver class" | |
| The solver's name. More... | |
| solvers.SolverTypes | SolverType = solvers.SolverTypes.Unknown |
| The type of the solver. More... | |
| EVENT | StepPerformed |
| Gets fired when an ODE solver performs an intermediate step. More... | |
| Public Attributes inherited from DPCMObject | |
| WorkspaceVariableName = "" | |
| The workspace variable name of this class. Optional. More... | |
| ID = "[]" | |
| An ID that allows to uniquely identify this DPCMObject (at least within the current MatLab session/context). More... | |
| PropertiesChanged = "[]" | |
| The Dictionary containing all the property settings as key/value pairs. More... | |
| Public Attributes inherited from handle | |
| addlistener | |
| Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More... | |
| notify | |
| Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More... | |
| delete | |
| Handle object destructor method that is called when the object's lifecycle ends. More... | |
| disp | |
| Handle object disp method which is called by the display method. See the MATLAB disp function. More... | |
| display | |
| Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More... | |
| findobj | |
| Finds objects matching the specified conditions from the input array of handle objects. More... | |
| findprop | |
| Returns a meta.property objects associated with the specified property name. More... | |
| fields | |
| Returns a cell array of string containing the names of public properties. More... | |
| fieldnames | |
| Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More... | |
| isvalid | |
| Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More... | |
| eq | |
| Relational functions example. See details for more information. More... | |
| transpose | |
| Transposes the elements of the handle object array. More... | |
| permute | |
| Rearranges the dimensions of the handle object array. See the MATLAB permute function. More... | |
| reshape | |
| hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More... | |
| sort | |
| ort the handle objects in any array in ascending or descending order. More... | |
| Static Protected Member Functions inherited from DPCMObject | |
| static function obj = | loadobj (obj, from) |
| Re-register any registered change listeners! More... | |
| static function obj = | loadobj (obj, from) |
| solvers.ExplEuler.ExplEuler | ( | double | MaxStep | ) |
Constructor for the explicit euler solver.
Specifying the dt parameter is optional, though not specifying will generate a warning that it should be set manually for each case.
| MaxStep | Maximum time step. Default: [] |
Definition at line 63 of file ExplEuler.m.
References solvers.SolverTypes.Explicit, solvers.BaseSolver.MaxStep, solvers.BaseSolver.Name, and solvers.BaseSolver.SolverType.
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Solves the ODE using the explicit Euler method.
There is a mex-implementation of the explicit euler scheme, unfortunately it is almost double the times slower than matlab! (So mexing files to get rid of for loops does not work well :-))
| odefun | A function handle to the ode function, satisfying the interface also required by matlab's explicit ode solvers. |
| t | The desired times \(t_0,\ldots,t_N\) as row vector. |
| x0 | The initial value \(x(0) = x_0\) for \(t=0\) |
| outputtimes | index vector indicating at which of the times in t the output is actually desired. The solution will be returned at \(t_0,\ldots,t_N\) = t(outputtimes). |
| x | The solution of the ode at the time steps \(t_0,\ldots,t_N\) as matrix. |
Sealed set to true. It cannot be overwritten. Definition at line 87 of file ExplEuler.m.
References dscomponents.AMassMatrix.evaluate(), solvers.BaseSolver.M, handle.notify, solvers.BaseSolver.RealTimeMode, and t.
1.8.6