C微分方程式

Question

この問題を解決する方法がわかりません。 プログラムは、無限ループで実行時から1年を表すために秒を使用します。ループの中で私はこの方程式を解く必要があります。

微分方程式：DP/DT = rPの（1-P/K） - HP

P（t）が（年）は時間tとともに変化集団です。

記号は意味を有する： DP/dtは Rが（年間分数増加など）の天然生殖増加率である（年間増加として）瞬時人口増加率である Kは、容量を運ぶ集団であります（環境がサポートできる最大人口） hは、人口が淘汰される率（年間損失として）

実行時間秒に応じて（秒は1年を表します）以下の正しい例

Simulation run time minute = 0; second = 3; millisec = 156 
Year of simulation = 3 
Rate of population change = 5180.209961 

私のコードが実行されたときにわかるように、正しい母集団の変化を計算する方法を理解することはできません。それは秒によって異なりますので、それは異なります。

#define _CRT_SECURE_NO_WARNINGS 

#include <stdio.h> 
#include <stdlib.h> 
#include <time.h> 

int main(void) 
    { 
    int option = 0; 
    float initialPopulation = 0; //starting population 
    float maximumPopulation = 0; //max population 
    float harvestingRate = 0; 
    float fractionGrowthPopulationRate = 0; 
    int minutes = 0; 
    int milliseconds = 0; 
    char quit; 
    int forever = 1; 
    float total = 0.0; 

    printf("Population Simulation\n"); 
    printf("1. run the simulation\n"); 
    printf("2. Quit\n"); 
    scanf("%d", &option); 

    if (option == 1) { 
     printf("ENTER SIMULATION PARAMETERS\n"); 
     printf("Initial population (typically 900000)?"); 
     scanf("%d", &initialPopulation); 
     printf("Maximum population the environment can support (typically 1000000)? \n"); 
     scanf("%d", &maximumPopulation); 
     printf("Initial harvesting rate (fraction per year - 0 for no\n harvesting)? "); 
     scanf("%f", &harvestingRate); 
     printf("Natural fractional growth population rate (typically 0.2 per year)?\n"); 
     scanf("%f", &fractionGrowthPopulationRate); 
     printf("\n"); 
    } 
    else if (option == 2) { 
     return 0; 
    } 

    while (forever != 'q') { 
     printf("starting simulation\n"); 

     clock_t t; 
     t = clock(); 
     //confused on how to code the formula 
     total = fractionGrowthPopulationRate * initialPopulation* (1 - initialPopulation/maximumPopulation) - harvestingRate*initialPopulation; 

     t = clock() - t; 
     int seconds = ((int)t)/CLOCKS_PER_SEC; // in seconds 

     printf("Simulation run time minute = %d; second = %d; millisec = %d\n", minutes, seconds, milliseconds); 

     printf("*****************************************************************\n"); 
     printf("Year of simulation = %d\n", seconds); //every seconds equals 1 year 
     printf("Rate of population change = %f\n", total); //total should be calculated 
     printf("*****************************************************************\n"); 
     printf("Press w/e to increase/decrease harvesting rate.\n"); 
     printf("Current harvesting rate : %f\n", harvestingRate); 
     printf("Press p/o to increase/decrease Max population supported.\n"); 
     printf("Current Max population : %d\n", maximumPopulation); 
     printf("Press k/l to increase/decrease growth rate.\n"); 
     printf("Current growth rate : %f\n", fractionGrowthPopulationRate); 
     printf("Press q to quit.\n"); 

     fflush(stdin); 
     scanf("%c", &forever); 
    } 
    return 0; 
    } 

Answer 1

次のコード：

1. はきれい
2. をコンパイルしたシミュレーションは、アカウントに前を取らなければならないイベント
3. ヒントの適切な順序付けが含まれてい
4. 別々の呼び出し可能な関数に機能を分離反復の結果。
5. 適切それでも最大の人口がここ

に達したときのためのコードを含めるようにしてください、processParameters()に「processParameters（） `関数

を完了する必要がありますユーザーの入力ミス

をチェック

#define _CRT_SECURE_NO_WARNINGS 
#include <stdio.h> // printf(), scanf() 
#include <stdlib.h> // exit(), EXIT_FAILURE 
//#include <time.h> 
#include <string.h> // strerror() 
#include <errno.h> // errno 

// prototypes 
void inputParameters(void); 
void processParameters(void); 
void displayResults(void); 
int handleMenu(void); 

// global data 
float initialPopulation = 0.0f; //starting population 
float maximumPopulation = 0.0f; //max population 
float harvestingRate = 0.0f; 
float fractionGrowthPopulationRate = 0.0f; 
float total = 0.0f; 

int minutes = 0; 
int seconds = 0; 
int milliseconds = 0; 


int main(void) 
{ 
    int quit = 0; 

    while(!quit) 
    { 
     int option = handleMenu(); 

     switch(option) 
     { 
      case 1: 
       inputParameters(); 
       processParameters(); 
       displayResults(); 
       break; 

      case 2: 
       quit = 1; 
       break; 

      default: 
       printf("invalid option: %d try again\n", option); 
       break; 
     } // end switch 
    } // end while 

    return 0; 
} // end function: main 


void inputParameters() 
{ 
    printf("ENTER SIMULATION PARAMETERS\n"); 

    printf("Initial population (typically 900000)?"); 
    if(1 != scanf("%f", &initialPopulation)) 
    { 
     fprintf(stderr, "input of initial population failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    printf("Maximum population the environment can support (typically 1000000)? \n"); 
    if(1 != scanf("%f", &maximumPopulation)) 
    { 
     fprintf(stderr, "input of maximum population failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    printf("Initial harvesting rate (fraction per year - 0 for no harvesting)? "); 
    if(1 != scanf("%f", &harvestingRate)) 
    { 
     fprintf(stderr, "input of omotoa; jarvestomg rate failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    printf("Natural fractional growth population rate (typically 0.2 per year)?\n"); 
    if(1 != scanf("%f", &fractionGrowthPopulationRate)) 
    { 
     fprintf(stderr, "input of initial population failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    printf("\n"); 
} // end function: inputParameters 


void displayResults() 
{ 
    printf("Simulation run time minute = %d; second = %d; millisec = %d\n", 
      minutes, seconds, milliseconds); 

    printf("*****************************************************************\n"); 
    printf("Year of simulation = %d\n", seconds); //every seconds equals 1 year 
    printf("Rate of population change = %f\n", total); //total should be calculated 
    printf("*****************************************************************\n"); 
    printf("Press w/e to increase/decrease harvesting rate.\n"); 
    printf("Current harvesting rate : %f\n", harvestingRate); 
    printf("Press p/o to increase/decrease Max population supported.\n"); 
    printf("Current Max population : %f\n", maximumPopulation); 
    printf("Press k/l to increase/decrease growth rate.\n"); 
    printf("Current growth rate : %f\n", fractionGrowthPopulationRate); 
    printf("Press q to quit.\n"); 
} // end function: displayResults 


int handleMenu() 
{ 
    int option = 0; 

    printf("\nPopulation Simulation\n"); 
    printf("1. run the simulation\n"); 
    printf("2. Quit\n"); 

    if(1 != scanf("%d", &option)) 
    { 
     fprintf(stderr, "scanf failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    return(option); 
} // end function: handleMenu 


void processParameters() 
{ 
    int simulationDuration = 0; 

    printf("how long is simulation to run:"); 
    if(1 != scanf("%d", &simulationDuration)) 
    { 
     fprintf(stderr, "input of simulation Duration failed due to: %s\n", strerror(errno)); 
     exit(EXIT_FAILURE); 
    } 

    printf("\nstarting simulation\n"); 

    total = initialPopulation; 
    for(int i=0; i<simulationDuration; i++) 
    { 
     //confused on how to code the formula 
     total = fractionGrowthPopulationRate * total * (1 - total/maximumPopulation) - harvestingRate*initialPopulation; 

     seconds = i; // in seconds 
    } 

    printf("\nsimulation complete\n"); 
} // end function: processParameters