Question

4.30 Write a MATLAB program that uses implicit Euler to integrate dx Use an initial condition y(0)-1 and integrate until x 2. What equations are needed for Newton's methiod? Is this solution becoming unstable?

Answer 1

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#calculates sum of digits recursively
SumDigits:

    sub     $sp,    $sp,    12                  #alloocate 12B on stack
    sw      $ra 0($sp)                      #save return address
    sw      $a0,    4($sp)                      #save argument

    beq     $a0,    $0, exit_sumdigits      #when there is no more digits return 0
    rem     $t0,    $a0,    10                  #get last digit
    sw      $t0,    8($sp)                      #save it on stack
    div     $a0,    $a0,    10                  #divide argument by 10
    jal     SumDigits                       #repeat procedure
    lw      $t0,    8($sp)                      #read digit from stack
    add     $v0,    $v0,    $t0             #add digit to previous result
    lw      $ra,    0($sp)                      #load return address
    addi    $sp,    $sp,    12                  #free stack
    jr      $ra                             #return

exit_sumdigits:
    li      $v0,    0                           #there are no more digits, return 0
    lw      $ra,    0($sp)                      #load return address
    addi    $sp,    $sp,    12                  #free stack
    jr      $ra                             #return

main:
    li      $a0,    75080                       #load number in $a0
    jal     SumDigits                           #call SumDigits

    move    $a0,    $v0                         #set a0 = result of SumDigits
    li      $v0,    1                           #set $v0 for print int system call
    syscall

    li      $v0,    10                          #set $v0 for exit system call
    syscall

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