function varargout = dsolve(varargin) %s=dsolve('方程1','方程2',...,'初始条件1','初始条件2',...,'自变量'). % 均用字符串方式表示,自变量缺省值为t. % 导数用D表示,2阶导数用D2表示,以此类推. % s返回解析解.方程组情形,s为一个符号结构. %narg = nargin; % The default independent variable is t. x = 't'; % Pick up the independent variable, if specified. if all(varargin{narg} ~= '='), x = varargin{narg}; narg = narg-1; end; % Concatenate equation(s) and initial condition(s) inputs into SYS. sys = varargin{1}; for k = 2: narg sys = ;; end % Break SYS into pieces. Each such piece, Dstr, begins with the first % character following a D and ends with the character preceding the % next consecutive D. Loop over each Dstr and do the following: % o add to the list of dependent variables % o replace derivative notation. E.g., D3y -- (D@@3)y % % A dependent variable is defined as a variable that is preceded by Dk, % where k is an integer. % % new_sys looks like: eqn(s), initial condition(s) (i.e., no brackets) % var_set looks like: { x(t), y2(t), ... } (i.e., with brackets) var_set = '{'; % string representing Maple set of dependent variables % Add dummy D so that last Dstr acts like all Dstr's d = ; new_sys = sys(1:d-1); % SYS rewritten with (D@@k)y notation for kd = 1:length(d)-1 Dstr = sys(d(kd)+1:d(kd+1)-1); iletter = find(isletter(Dstr)); % index to letters in Dstr % Replace Dky with (D@@k)y if iletter(1)==1 % First derivative case (Dy) new_sys = ; else new_sys = ; end % Store the dependent variable. Find this variable by looking at the % characters following the derivative order and pulling off the first % consecutive chunk of alphanumeric characters. Dstr1 = Dstr(iletter(1):end); ialphanum = find(~isletter(Dstr1) (Dstr1 '0' | Dstr1 '9')); var_set = ; end % Get rid of duplicate entries in var_set var_set(end) = '}'; var_set = maple( ); % Generate var_str, the Maple string representing the set of dependent % variables. % Replace all dependent variables with their functional equivalents, % i.e., replace y - (y)(x). % Break the system string into its equation and initial condition parts. % This is done by looking for the first occurrence of y(, where y is a % dependent variable. indx_ic = length(new_sys); % points to starting character of ic string ic_str = ; % preceding comma delimits variable vars(find(vars==' '))= ; % Look for first occurrence of v(. If it's before the first occurrence % of the previous dependent variable, change value of indx_ic and % shorten the equation string. indx = findstr(eq_str, ); % index to current dependent var. if isempty(indx), indx = indx_ic; end indx_ic = min(indx_ic,indx(1)); eq_str = new_sys(1:min(indx_ic)); end % Finish var_str var_str(end) = '}'; % Stuff after the last comma belongs in the initial condition string if indx_ic length(new_sys) last_comma = max(find(eq_str==',')); ic_str = new_sys(last_comma:end); eq_str = eq_str(1: last_comma-1); end % In the equation string, replace all occurrences of y with (y)(x). for j = 1:length(kommas)-1 v = vars(kommas(j)+1:kommas(j+1)-1); m = length(v); e = length(eq_str); for k = fliplr(findstr(v,eq_str)) if k+m e | ~isvarname(eq_str(k:k+m)) eq_str = ; end end end % In the ic string, replace all occurrences of y with (y). for j = 1:length(kommas)-1 v = vars(kommas(j)+1:kommas(j+1)-1); m = length(v); e = length(ic_str); for k = fliplr(findstr(v,ic_str)) if k+m e | ~isvarname(ic_str(k:k+m)) ic_str = ; end end end % Convert system to rational form and solve = maple('dsolve', ... , var_str, 'explicit'); if stat error(R) end % If no solution, give up. if isempty(R) | ~isempty(findstr(R,'DESol')) warning('Explicit solution could not be found.'); varargout = cell(1,nargout); varargout{1} = sym( ; % Parse the result. if R(1) ~= '{', R = ; end vars(1) = ' '; vars = maple('sort',vars); vars(1) = '{'; vars(end) = '}'; nvars = sum(commas(vars))+1; if nvars == 1 nargout = 1 % One variable and at most one output. % Return a single scalar or vector sym. S = sym( ; end varargout{1} = S; else % Several variables. % Create a skeleton structure. c = ; S = ); end % Complete the structure. c = ; for p = find(R == '=') q = max(c(cp)); v = trim(R(q+1:p-1)); v(findstr(v,'('):findstr(v,')')) = ); end if nargout = 1 % At most one output, return the structure. varargout{1} = S; elseif nargout == nvars % Same number of outputs as variables. % Match results in lexicographic order to outputs. v = fieldnames(S); for j = 1:nvars varargout{j} = getfield(S,v{j}); end else error( ) end end function s = trim(s); %TRIM TRIM(s) deletes any leading or trailing blanks. while s(1) == ' ', s(1) = ; end function c = commas(s) %COMMAS COMMAS(s) is true for commas not inside parentheses. p = cumsum((s == '(') - (s == ')')); c = (s == ',') (p == 0);
标签: 方程
