- fixed movie creation in eval_methods.m

- added gif animation

+fractional_steps/step.m

@@ -1,39 +1,52 @@
-function [pressure_output, N_steps] = step( pressure_input, f_s, delta_z, a, b, order )
+function [ pressure_output, N_steps ] = step( pressure_input, f_s, delta_z, a, b, order )
+% Strang-Marchuk splitting step
+%
 % author: Martin Schiffner
 % date: 2009-03-30
-% modified: 2020-05-06
+% modified: 2020-05-07
 
+%--------------------------------------------------------------------------
+% 1.) check arguments
+%--------------------------------------------------------------------------
+
+%--------------------------------------------------------------------------
+% 2.) compute splitting step
+%--------------------------------------------------------------------------
+%
 N_samples = numel(pressure_input);
 ksi = 0.5;                          %factor used in finite difference scheme (0.5 = Crank-Nicolson method)
 method_interp = 'linear';           %method which is used for interpolation in solution to nonlinear problem
 
+%
 switch order
 
     case 0
         % solve linear diffusion equation for delta_z / 2 (adjustable finite difference scheme)
         pressure_input = fractional_steps.diffusion( pressure_input, f_s, N_samples, delta_z / 2, a, ksi );
 
         % solve nonlinear equation for delta_z    
-        [pressure_input, N_steps] = fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z, b, method_interp );
+        [ pressure_input, N_steps ] = fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z, b, method_interp );
 
         % solve linear diffusion equation for delta_z / 2 (adjustable finite difference scheme)
         pressure_output = fractional_steps.diffusion( pressure_input, f_s, N_samples, delta_z / 2, a, ksi );
 
     case 1
         % solve nonlinear equation for delta_z / 2
-        [pressure_input, N_steps_1] = fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z / 2, b, method_interp );
+        [ pressure_input, N_steps_1 ] = fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z / 2, b, method_interp );
 
         % solve linear diffusion equation for delta_z (adjustable finite difference scheme)
         pressure_input = fractional_steps.diffusion( pressure_input, f_s, N_samples, delta_z, a, ksi );
 
         % solve nonlinear equation for delta_z / 2
-        [pressure_output, N_steps_2] =  fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z / 2, b, method_interp );
+        [ pressure_output, N_steps_2 ] =  fractional_steps.nonlinear( pressure_input, f_s, N_samples, delta_z / 2, b, method_interp );
 
         N_steps = [N_steps_1, N_steps_2];
 
     otherwise
+
         % display error message
-        error('burgers_frac_steps: invalid argument order in fractional steps scheme');     
+        error('burgers_frac_steps: invalid argument order in fractional steps scheme');
+
 end
 
 end % function [pressure_output, N_steps] = step( pressure_input, f_s, delta_z, a, b, order )

README.md

@@ -18,10 +18,47 @@ the nonlinear propagation of
 plane ultrasonic waves in
 homogeneous viscous fluids.
 
-The model is potentially interesting for
-fast tissue harmonic imaging (THI) or
+Its incorporation into
+fast tissue harmonic imaging or
 the detection of
-ultrasound contrast agents.
+ultrasound contrast agents potentially improves
+these imaging modes.
+Moreover,
+the decompositions of
+arbitrary types of
+waves into
+steered plane waves permit
+the application of
+this model
+the Burgers equation to
+other types of waves.
+
+## Content
+
+The script "eval_methods.m" compares
+both methods by evaluating
+various error metrics.
+It additionally creates
+a movie illustrating
+the deformation of
+the wave and
+the accompanying generation of
+harmonics.
+
+The package +volterra contains
+the functions for
+the proposed Volterra polynomial, whereas
+the package +fractional_steps contains
+the functions for
+the fractional steps reference method.
+
+## Results
+
+The following animation depicts
+the result of
+the 10th-degree Volterra polynomial.
+
+![Animation](./burgers_propagation_hp.gif)
 
 ## References :notebook: